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olur."]},"beginTime":53,"endTime":168,"href":"/video/preview/8860905618147943600?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=53&ask_summarization=1"},{"index":2,"title":"Olasılık Formülü","list":{"type":"unordered","items":["Olasılık (P) formülü: İstenen durum sayısı / Örnek uzay sayısıdır.","Olasılığın en önemli özelliği istenen durumları tüm durum sayısına bölmektir."]},"beginTime":168,"endTime":219,"href":"/video/preview/8860905618147943600?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=168&ask_summarization=1"},{"index":3,"title":"Olasılığın Özellikleri","list":{"type":"unordered","items":["Bir olayın olasılığı muhakkak 0,5 ile 1 arasında bir sayı olmak zorundadır.","0 şeklinde bir olasılık imkansız olayı, 1 şeklinde bir olasılık kesin olayı ifade eder.","Bir olayın olasılığı ile olmamasının toplamı muhakkak 1 olmak zorundadır.","Olayın olmasını bulmak için bazen olmamasını bulup 1'den çıkarmak daha kolaydır."]},"beginTime":219,"endTime":343,"href":"/video/preview/8860905618147943600?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=219&ask_summarization=1"},{"index":4,"title":"Bağımsız Olaylar","list":{"type":"unordered","items":["Bağımsız olaylar, birbirini ilgilendirmeyen, birbirinden bağlantısız olaylardır.","Bağımsız olayların beraber gerçekleşmesi için P(A∩B) = P(A) × P(B) formülü kullanılır.","\"Ve\" cümlesi kullanıldığında bağımsız olayların beraber gerçekleşmesi için bu formül kullanılır."]},"beginTime":343,"endTime":516,"href":"/video/preview/8860905618147943600?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=343&ask_summarization=1"},{"index":5,"title":"Ayrık Olaylar","list":{"type":"unordered","items":["Ayrık olaylar, kesişimleri boş küme olan olaylardır.","Ayrık olayların kesişim olasılığı 0'dır.","Ayrık olayların birleşimi için P(A∪B) = P(A) + P(B) formülü kullanılır."]},"beginTime":516,"endTime":631,"href":"/video/preview/8860905618147943600?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=516&ask_summarization=1"},{"index":6,"title":"Koşullu Olasılık","list":{"type":"unordered","items":["Koşullu olasılık, \"şartlı olasılık\" olarak da adlandırılır.","Koşullu olasılık sorularında \"şart bilindiğine göre\" şeklinde bir cümle kullanılır.","Koşullu olasılık formülü: P(A|B) = P(A∩B) / P(B) şeklindedir."]},"beginTime":631,"endTime":775,"href":"/video/preview/8860905618147943600?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=631&ask_summarization=1"},{"index":7,"title":"Olasılık Formülleri ve İşlemsel Sorular","list":{"type":"unordered","items":["A birleşim B formülü P(A birleşim B) = P(A) + P(B) - P(A kesişim B) olarak verilmiştir.","Ayrık iki olayın kesişimleri boş küme olduğundan, A birleşim B = P(A) + P(B) formülü kullanılır.","Bir olayın olma ve olmama olasılıklarının toplamı 1'e eşittir."]},"beginTime":783,"endTime":954,"href":"/video/preview/8860905618147943600?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=783&ask_summarization=1"},{"index":8,"title":"Olasılık Problemleri","list":{"type":"unordered","items":["Olasılık problemlerinde istenen durum ve tüm durum özellikleri bilinerek çözüm yapılır.","Bir madeni paranın havaya atılması deneyinde yazı gelme olasılığı 1/2'dir.","Bir zarın havaya atılması deneyinde asal sayı gelme olasılığı 3/6'dır."]},"beginTime":954,"endTime":1140,"href":"/video/preview/8860905618147943600?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=954&ask_summarization=1"},{"index":9,"title":"Çoklu Para Atma Problemleri","list":{"type":"unordered","items":["Bir madeni paranın üç defa havaya atılma olayında iki yazı bir tura gelme olasılığı 3/8'dir.","Sırasıyla yazı tura yazı gelme olasılığı 1/8'dir.","En çok iki tura gelme olasılığı, üç tura gelme olasılığını 1'den çıkararak 7/8 olarak bulunur."]},"beginTime":1140,"endTime":1398,"href":"/video/preview/8860905618147943600?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=1140&ask_summarization=1"},{"index":10,"title":"Sınıf Öğrencileri Problemi","list":{"type":"unordered","items":["Dört kız altı erkek öğrenciden oluşan bir sınıfta bir kişi seçiliyor.","Seçilen kişinin kız öğrenci olma olasılığı 4/10 = 2/5'tir.","Tek kişi seçiliyorsa, paydaya tüm durum (10 öğrenci) ve payda seçilen nesne sayısı (4 kız) yazılır."]},"beginTime":1398,"endTime":1446,"href":"/video/preview/8860905618147943600?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=1398&ask_summarization=1"},{"index":11,"title":"Zar Atma Olasılıkları","list":{"type":"unordered","items":["İkizler aynı anda havaya atıldığında üst üste gelen sayıların çarpımının tek sayı olma olasılığı 1/4'tür.","İki zarın toplamlarının altı olma olasılığı 5/36'dır.","İki zarın toplamlarının asal sayı olma olasılığı 1/4'tür."]},"beginTime":1451,"endTime":1643,"href":"/video/preview/8860905618147943600?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=1451&ask_summarization=1"},{"index":12,"title":"Diğer Olasılık Problemleri","list":{"type":"unordered","items":["İki zarın toplamlarının dörtten küçük olma olasılığı 1/12'dir.","Yalnızca birinin dört olma olasılığı 5/18'dir.","Hileli bir para için yazı gelme olasılığı tura gelme olasılığının üç katı olduğunda, yazı-yazı gelme olasılığı 9/16'dır."]},"beginTime":1643,"endTime":1841,"href":"/video/preview/8860905618147943600?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=1643&ask_summarization=1"},{"index":13,"title":"Boncuk Seçme Problemi","list":{"type":"unordered","items":["Bir torbada üç mavi ve yedi siyah boncuk vardır.","Torbadan rastgele iki boncuk seçildiğinde, çekilen boncukların ikisinin de mavi olma olasılığı 1/15'tir."]},"beginTime":1841,"endTime":1893,"href":"/video/preview/8860905618147943600?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=1841&ask_summarization=1"},{"index":14,"title":"Olasılık Problemleri Çözümü","list":{"type":"unordered","items":["Birinci yöntemde, bir nesne seçme olasılığı paydaya tüm durum, yukarıya seçilen nesne sayısını yazarak hesaplanır.","Farklı renkte nesne seçme olasılığı için, 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Video sonunda dizi konusunun sonlandığı ve gelecek konuların (logaritma, trigonometri) tekrar edileceği bilgisi verilmektedir."]},"endTime":2901,"title":"Aritmetik Dizi Matematik Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Aritmetik Dizi Tanımı ve Özellikleri","list":{"type":"unordered","items":["Aritmetik dizi, artış miktarının hep aynı olması ve ortak bir farkla artması gereken bir dizi türüdür.","Aritmetik dizide, bir sonraki terimden bir önceki terim çıkarıldığında oluşan fark değeri \"d\" ile gösterilir ve ortak fark olarak adlandırılır.","Aritmetik dizinin herhangi bir terimi, ilk terim (a₁) cinsinden a₁ + (n-1)d şeklinde yazılabilir."]},"beginTime":0,"endTime":215,"href":"/video/preview/17811458413787296775?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=0&ask_summarization=1"},{"index":1,"title":"Aritmetik Dizinin Diğer Özellikleri","list":{"type":"unordered","items":["Aritmetik dizinin herhangi bir terimi, farklı terimler cinsinden de yazılabilir: aₙ = aₖ + (n-k)d şeklinde.","İlk n terim toplamı (Sₙ) formülü: Sₙ = n × (a₁ + aₙ) / 2 veya Sₙ = n/2 × (2a₁ + (n-1)d).","Aritmetik dizide eşit uzaklıktaki terimlerin aritmetik ortalaması ortadaki terimi verir veya eşit uzaklıktakilerin toplamı hep aynı sayı çıkar."]},"beginTime":215,"endTime":741,"href":"/video/preview/17811458413787296775?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=215&ask_summarization=1"},{"index":2,"title":"Aritmetik Dizi Problemi Çözümü","list":{"type":"unordered","items":["İki ayrı aritmetik dizi denklemi verilmiş: a₁ + a₉ = 12 ve a₅ + a₁₃ = 28.","Denklemler a₁ cinsinden yazılarak ortak fark d = 2 ve a₁ = -2 bulunmuştur.","a₇ terimi a₁ cinsinden a₇ = a₁ + 6d formülüyle 10 olarak hesaplanmıştır."]},"beginTime":747,"endTime":950,"href":"/video/preview/17811458413787296775?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=747&ask_summarization=1"},{"index":3,"title":"Üç Basamaklı En Küçük Terim Problemi","list":{"type":"unordered","items":["a₁₁ = 43 ve a₅ = 19 olan aritmetik dizinin ortak farkı d = 4 ve a₁ = 3 bulunmuştur.","Dizinin genel terimi aₙ = 3 + 4(n-1) olarak oluşturulmuştur.","Üç basamaklı en küçük terim için 4n-1 ≥ 100 denkleminden n ≥ 26 bulunmuştur ve a₂₆ = 103 olarak hesaplanmıştır."]},"beginTime":950,"endTime":1176,"href":"/video/preview/17811458413787296775?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=950&ask_summarization=1"},{"index":4,"title":"İki Dizinin Eşit Terimleri Problemi","list":{"type":"unordered","items":["aₙ = 4n-1 ve bₙ = -3n + 146 denklemleri oluşturulmuştur.","İki dizinin genel terimleri eşitlenerek 7n = 147 denklemi çözülmüştür.","n = 21 olarak bulunmuş, yani 21. terimler birbirine eşittir."]},"beginTime":1176,"endTime":1386,"href":"/video/preview/17811458413787296775?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=1176&ask_summarization=1"},{"index":5,"title":"Çizgi Uzunlukları Problemi","list":{"type":"unordered","items":["Tuncel A noktasından başlayarak 2 mm'lik bir çizgi çizmiş ve her sonraki çizgiyi bir öncekinden 3 mm daha uzun olarak çizmiştir.","İlk 24 çizginin toplamı S₂₄ = 12 × (2 + 73) formülüyle hesaplanmıştır.","İlk 24 çizginin toplam uzunluğu 876 mm olarak bulunmuştur."]},"beginTime":1386,"endTime":1581,"href":"/video/preview/17811458413787296775?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=1386&ask_summarization=1"},{"index":6,"title":"Aritmetik Dizilerde a₁ Cinsinden Yazma","list":{"type":"unordered","items":["Aritmetik dizide a₇ + a₁₁ + a₂₁ / a₁₃ oranı sorulduğunda, tüm terimler a₁ cinsinden yazılmalıdır.","a₇ = a₁ + 6d, a₁₁ = a₁ + 10d, a₂₁ = a₁ + 20d şeklinde yazıldığında, toplam 3a₁ + 36d = a₁ + 12d olur.","Oran 3a₁ + 36d / a₁ + 12d = 3 olarak bulunur."]},"beginTime":1590,"endTime":1716,"href":"/video/preview/17811458413787296775?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=1590&ask_summarization=1"},{"index":7,"title":"Negatif Değerli İlk Terim Bulma","list":{"type":"unordered","items":["İlk üç terimi 4x + 7, 2x + 5, 5x + 8 olan aritmetik dizide, x = 9 olarak bulunur.","Dizi 29, 23, 17 şeklinde azalarak gider ve genel terimi aₙ = 29 - 6d olur.","Negatif değerli ilk terim için aₙ \u003c 0 denklemini çözerken, n = 6 olduğunda a₆ = -1 olarak bulunur."]},"beginTime":1716,"endTime":1946,"href":"/video/preview/17811458413787296775?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=1716&ask_summarization=1"},{"index":8,"title":"Aritmetik Dizilerde Toplam ve Terim Bulma","list":{"type":"unordered","items":["S₂₁ - S₂₄ = 42 eşitliğinde, S₂₁ = S₁₄ + a₂₁ + a₂₀ + a₁₉ + a₁₈ + a₁₇ + a₁₆ + a₁₅ şeklinde yazılır.","Eşit uzaklıktakilerin toplamı ortadakinin iki katı olduğundan, 7a₁₈ = 42 olur ve a₁₈ = 6 olarak bulunur.","Bu özellik, aritmetik dizilerde sıkça kullanılan ve soruları çözerken pratik sağlayan bir nottur."]},"beginTime":1946,"endTime":2083,"href":"/video/preview/17811458413787296775?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=1946&ask_summarization=1"},{"index":9,"title":"Aritmetik Dizilerde Terim İlişkisi","list":{"type":"unordered","items":["a₄ = 11 ve S₁₀ = 145 verilen aritmetik dizide, S₁₀ = 10 = (a₁ + a₁₀) / 2 = 29 olur.","Eşit uzaklıktakilerin toplamı ortadakinin iki katı olduğundan, a₄ + a₇ = 29 olur.","a₄ = 11 olduğundan, a₇ = 18 olarak bulunur."]},"beginTime":2083,"endTime":2297,"href":"/video/preview/17811458413787296775?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=2083&ask_summarization=1"},{"index":10,"title":"Öncülü Sorular","list":{"type":"unordered","items":["Öncülü sorular, öğrencilerin bilgi seviyesini ve dikkat seviyesini kontrol eden, daha tehlikeli soru tipleridir.","Öğrenciler normal işlemsel soruları daha rahat yaparken, öncüllü sorularda takılıp yanlış cevabı işaretleyebilirler.","x, y, z reel sayılar ve aritmetik dizi oluşturan ardışık üç terim ise, x + z = 2y olur."]},"beginTime":2297,"endTime":2377,"href":"/video/preview/17811458413787296775?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=2297&ask_summarization=1"},{"index":11,"title":"Aritmetik Dizi Özellikleri","list":{"type":"unordered","items":["Bir aritmetik dizinin ardışık üç terimi için, eşit uzaklıktakilerin toplamı ortadakinin iki katı olmalıdır.","Verilen ifadelerden birinci, ikinci ve üçüncü maddeler aritmetik dizinin ardışık üç terimini oluşturabilir.","Aritmetik dizi oluşturmak için sadece bir tane sağlayan durum yeterlidir."]},"beginTime":2380,"endTime":2558,"href":"/video/preview/17811458413787296775?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=2380&ask_summarization=1"},{"index":12,"title":"Çember Kesişim Sorusu","list":{"type":"unordered","items":["Birinci adımda bir çemberle başlanıp her adımda çemberin sağına iki noktada kesişecek biçimde bir çember çizilmiştir.","Birinci adımda 1 çember ve 0, ikinci adımda 2 çember ve 2 kesişim noktası, üçüncü adımda 3 çember ve 4 kesişim noktası vardır.","Yirmiüçüncü adımdaki çemberlerin ve kesişim noktalarının toplamı 67'dir."]},"beginTime":2558,"endTime":2790,"href":"/video/preview/17811458413787296775?parent-reqid=1769504688838422-4588041334151348681-balancer-l7leveler-kubr-yp-klg-95-BAL&text=MATH+With+Iskender&t=2558&ask_summarization=1"},{"index":13,"title":"Konu Önerileri","list":{"type":"unordered","items":["Aritmetik dizi konusu basit ve kısa özelliklere sahip, bol soru çözümüyle pekiştirilebilir.","Dizi konusu (aritmetik dizi, geometrik dizi) tamamlandıktan sonra logaritma ve trigonometri konuları işlenecektir.","AYT konularını sağlamlaştırıp, TYT ve AYT'yi eşit bir şekilde çalışarak sınava hazırlanmak tavsiye 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