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Dersin sonunda öğrencilere TYT matematik soru bankasından ardışık sayılar temel tanım testi çözülmesi ödevi verilmektedir."]},"endTime":3479,"title":"70 Günde TYT Matematik Kampı: Ardışık Sayılar","beginTime":0}],"fullResult":[{"index":0,"title":"TYT Matematik Kampı - Ardışık Sayılar","list":{"type":"unordered","items":["TYT matematik kampının dördüncü gününde temel kavramların beşinci alt başlığı olan ardışık sayılar konusu ele alınacak.","Bu videoda ardışık sayılar, ikinci videoda ise ardışık sayı örüntüleri anlatılacak.","Kamp programı kısmında ardışık sayılar konusu sayfa 19-21'de yer alıyor ve soru bankasından temel tanım testi 1-2 (sayfa 20-23) çözülecek."]},"beginTime":0,"endTime":98,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=0&ask_summarization=1"},{"index":1,"title":"Ardışık Sayıların Tanımı","list":{"type":"unordered","items":["Ardışık sayılar, aralarındaki fark sabit olan sayılardır ve genel olarak bir bir artan sayılar olarak tanımlanabilir.","Ardışık sayı kavramı sadece pozitif sayılarda değil, aynı zamanda negatif tam sayılarda da tanımlıdır.","Ardışık tek sayılar (1, 3, 5, 7, 9) ve ardışık çift sayılar (2, 4, 6, 8) vardır."]},"beginTime":98,"endTime":170,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=98&ask_summarization=1"},{"index":2,"title":"Ardışık Sayıların Özellikleri","list":{"type":"unordered","items":["Ardışık iki sayı arasındaki fark ya 1'dir ya da -1'dir çünkü hangi sayıdan hangisini çıkardığımız bilinmemektedir.","Ardışık iki tek ya da iki çift sayı arasındaki fark ya 2'dir ya da -2'dir.","Ardışık sayılar konusu TYT'de çok işe yarayacak ve AYT matematik konularında da sıkça karşımıza çıkacaktır."]},"beginTime":170,"endTime":223,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=170&ask_summarization=1"},{"index":3,"title":"Örnek Sorular","list":{"type":"unordered","items":["İlk örnek soruda x, y ve z ardışık tek sayılar ve x \u003c y \u003c z olmak üzere verilen işlemin sonucu 0'dır.","İkinci örnek soruda a tek bir doğal sayıdır ve 3a+3 sayısından önce gelen ardışık iki tek sayının toplamı 56 ise, 3a sayısından sonra gelen ardışık iki çift sayının toplamı 58'dir."]},"beginTime":223,"endTime":444,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=223&ask_summarization=1"},{"index":4,"title":"Ardışık Çift Sayılar Problemi","list":{"type":"unordered","items":["Ardışık üç pozitif çift sayının en küçüğü a, en büyüğü b ve ortancası c ise, a+3b=92 olduğunda c'nin değeri 22 olarak bulunur.","Ardışık sayılar arasındaki fark 2 olduğundan, c=a+2 ve b=a+4 şeklinde ifade edilir.","Denklem çözülerek a=20 bulunur ve c=20+2=22 olarak hesaplanır."]},"beginTime":445,"endTime":544,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=445&ask_summarization=1"},{"index":5,"title":"Ardışık İki Sayı Problemi","list":{"type":"unordered","items":["2a+5 ile 3a-9 sayıları ardışık iki sayı olduğunda, a'nın alabileceği değerler toplamı 28 olarak bulunur.","Ardışık iki sayı arasındaki fark 1 veya -1 olabilir, bu durumda iki farklı denklem kurulur.","İlk denklemde a=13, ikinci denklemde a=15 bulunur ve toplamları 28 olarak hesaplanır."]},"beginTime":544,"endTime":718,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=544&ask_summarization=1"},{"index":6,"title":"Ardışık Beş Doğal Sayı Problemi","list":{"type":"unordered","items":["Ardışık beş doğal sayının toplamı 95 olduğunda, bu sayıların en büyüğü en küçüğünün toplamı 38 olarak bulunur.","Sayılar x+1, x+2, x+3, x+4, x+5 şeklinde ifade edilir.","Denklem çözülerek x=16 bulunur, en büyük sayı 21, en küçük sayı 17 ve toplamları 38 olarak hesaplanır."]},"beginTime":718,"endTime":817,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=718&ask_summarization=1"},{"index":7,"title":"Ardışık İki Tek Doğal Sayı Problemi","list":{"type":"unordered","items":["Ardışık iki tek doğal sayının kareleri farkı 40 olduğunda, bu sayıların toplamı 20 olarak bulunur.","Sayılar x ve x+2 şeklinde ifade edilir ve denklem kurulur.","Denklem çözülerek x=9 bulunur, sayılar 9 ve 11 olup toplamları 20 olarak hesaplanır."]},"beginTime":817,"endTime":898,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=817&ask_summarization=1"},{"index":8,"title":"Ardışık Sayılar ve Üçüz Sayılar","list":{"type":"unordered","items":["Ardışık üç doğal sayının çarpımı şeklinde yazılan sayılara üçüz sayı denir.","Örneğin, 8×9×10=720 olduğundan 720 üçüz sayıdır.","Ardışık üç sayının çarpımı şeklinde yazılan bir sayı, ardışık üç sayının çarpımı şeklinde yazılacaksa üçüz sayı olur."]},"beginTime":902,"endTime":954,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=902&ask_summarization=1"},{"index":9,"title":"Üçüz Sayı Problemi","list":{"type":"unordered","items":["x ve y sıfırdan farklı birer üçüz sayı olmak üzere x=2y eşitliği sağlanıyor ve x ile y arasında başka bir üçüz sayı olmadığına göre x kaçtır?","x sayısı a×(a+1)×(a+2) şeklinde yazılabilir ve y sayısı a×(a-1)×(a+1) şeklinde yazılabilir.","x=2y olduğundan a=4 bulunur ve x=120, y=60 olarak hesaplanır."]},"beginTime":954,"endTime":1141,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=954&ask_summarization=1"},{"index":10,"title":"Ardışık Tek Sayılar Problemi","list":{"type":"unordered","items":["A kümesi altı ardışık tek doğal sayıdan oluşmaktadır ve kümedeki elemanların toplamı en büyük elemanın dört katına eşittir.","A kümesi a+2, a+4, a+6, ..., a+12 şeklinde yazılabilir.","Kümedeki elemanların toplamı 6a+42, en büyük elemanın dört katı 4(a+12) olduğundan a=3 bulunur ve en büyük eleman 15'tir."]},"beginTime":1141,"endTime":1262,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=1141&ask_summarization=1"},{"index":11,"title":"Terim Sayısı ve Ortanca Terim","list":{"type":"unordered","items":["Terim sayısı, son terim eksi ilk terim bölü artış miktarı artı bir formülüyle bulunur.","Ortanca terim, son terim artı ilk terim bölü iki formülüyle bulunur.","Terim sayısı çift olduğunda ortanca terim ortadaki terimlerin ortalaması olur."]},"beginTime":1262,"endTime":1473,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=1262&ask_summarization=1"},{"index":12,"title":"Ardışık Sayıların Toplamı","list":{"type":"unordered","items":["Ardışık sayıların toplamı, terim sayısı çarpı ortanca terim formülüyle bulunur.","Örneğin, 4'ten 88'e kadar olan ardışık sayıların toplamı 46×13=598'dir.","Ardışık 11 çift sayının toplamı 286 olduğunda, en büyük sayı 36'dır."]},"beginTime":1476,"endTime":1732,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=1476&ask_summarization=1"},{"index":13,"title":"Ardışık Sayılarda Değişim","list":{"type":"unordered","items":["Bir ardışık sayı dizisinde her terim 2 azaltıldığında, toplam 31×2=62 azalır.","Ardışık sayılarda her terim 2 azaltıldığında, toplam 31×2=62 azalır."]},"beginTime":1732,"endTime":1822,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=1732&ask_summarization=1"},{"index":14,"title":"Özel Formüller","list":{"type":"unordered","items":["1'den n'ye kadar olan ardışık sayıların toplamı formülü: n×(n+1)/2'dir.","Ardışık çift sayıların toplamı formülü: n×(n+1)'dir.","Ardışık tek sayıların toplamı formülü: n²'dir."]},"beginTime":1822,"endTime":1951,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=1822&ask_summarization=1"},{"index":15,"title":"Örnek Soru Çözümü","list":{"type":"unordered","items":["1'den 45'e kadar olan ardışık tek sayıların toplamı 23²=529'dur.","2'den 48'e kadar olan ardışık çift sayıların toplamı 24×25=600'dür.","İki toplam arasındaki fark 529-600=71'dir."]},"beginTime":1951,"endTime":2026,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=1951&ask_summarization=1"},{"index":16,"title":"Ardışık Sayılar Problemleri","list":{"type":"unordered","items":["A ve B arasındaki fark, A'dan B'yi çıkartarak veya ayrı ayrı bulup birbirinden çıkartarak hesaplanabilir.","Ardışık sayıların toplamı, terim sayısını ve artış miktarını kullanarak hesaplanabilir.","Ardışık tek sayıların toplamı, 1'den başlayıp 2m-1'e kadar giden ardışık sayıların toplamı olarak m² olarak ifade edilebilir."]},"beginTime":2029,"endTime":2198,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=2029&ask_summarization=1"},{"index":17,"title":"Ardışık Sayılar Problemleri","list":{"type":"unordered","items":["Ardışık sayıların toplamı, ikili ikili alınarak ve toplam terim sayısı hesaplanarak bulunabilir.","Bir sokakta üst taraftaki evler ardışık tek sayılarla, alt taraftaki evler ardışık çift sayılarla numaralandırıldığında, evlerin numaraları arasındaki farklar hesaplanabilir.","Ardışık tek sayıların toplamı, ardışık çift sayıların toplamından daha kolaydır."]},"beginTime":2198,"endTime":2402,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=2198&ask_summarization=1"},{"index":18,"title":"Ardışık Sayılar Problemleri","list":{"type":"unordered","items":["Ardışık tek sayılar arasındaki fark 4'tür, bu fark kullanılarak sayılar bulunabilir.","Ardışık çift sayılar arasındaki fark 2'dir, bu fark kullanılarak sayılar bulunabilir.","Ardışık sayıların toplamı, sayıların değerlerini bulup toplayarak hesaplanabilir."]},"beginTime":2402,"endTime":2611,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=2402&ask_summarization=1"},{"index":19,"title":"Matematik Problemi Çözümü","list":{"type":"unordered","items":["İki p artı üç ile yirmisekiz ardışık tam sayılardır ve üç q eksi iki ile onsekiz ardışık çift sayılardır.","p'nin az olması için iki p artı üç'ü küçük sayı olarak seçerek p=12 bulunur.","Üç q eksi iki'yi küçük sayı olarak seçerek q=6 bulunur ve p+q toplamı 18 olarak hesaplanır."]},"beginTime":2614,"endTime":2738,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=2614&ask_summarization=1"},{"index":20,"title":"Ev Numaraları Problemi","list":{"type":"unordered","items":["Aynı sokakta yan yana sıralanmış ve numaraları arasındaki fark eşit olacak şekilde numaralandırılmış altı tane ev gösterilmiştir.","Ardışık sıralanan sayı dizilerinde kendisine eşit uzaklıkta olan terimlerin aritmetik ortalaması o terimi verir.","Tüm evlerin numaraları toplamı 87 olarak bulunur."]},"beginTime":2738,"endTime":2865,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=2738&ask_summarization=1"},{"index":21,"title":"Daire Problemi","list":{"type":"unordered","items":["Yan yana duran iki dairedeki sayıların toplamı kendilerine bağlı olan alttaki daire yazılıyor.","En üstte bulunan mavi dairelere soldan sağa doğru olmak üzere küçükten büyüğe doğru ardışık üç tam sayı yazılıyor.","a ve b toplamı 49 olarak bulunur."]},"beginTime":2865,"endTime":2944,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=2865&ask_summarization=1"},{"index":22,"title":"Ardışık Sayılar Problemi","list":{"type":"unordered","items":["Ardışık üç pozitif çift sayının çarpımı şeklinde yazılabilen sayılara \"art arda sayılar\" denir.","a art arda sayı olmak üzere, a sayısını oluşturan çift sayıların her birine bölerek elde edilen bölümlerin toplamı 188'dir.","Problemin çözümünde x'in çift sayı olduğunu ve en küçük çift sayıdan başlayarak (x=6) denendiğinde 188'e ulaşıldığı gösterilmiştir."]},"beginTime":2973,"endTime":3166,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=2973&ask_summarization=1"},{"index":23,"title":"Ardışık Sayılar Probleminin Çözümü","list":{"type":"unordered","items":["Problemin uzun çözümünde x² + 12x - 180 = 0 denkleminin çarpanlara ayrılarak x = 6 olarak bulunması gösterilmiştir.","Ardışık pozitif üç çift sayının çarpımı olduğu için x'in pozitif olması gerektiği vurgulanmıştır.","Ardışık sayılardan genellikle bölme bölünebilme, sayı basamakları, EBOB, OKEK ve üslü sayılar konularında sorular sorulduğu belirtilmiştir."]},"beginTime":3166,"endTime":3281,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=3166&ask_summarization=1"},{"index":24,"title":"Kardeş Sayılar Problemi","list":{"type":"unordered","items":["Ardışık iki ya da üç pozitif tam sayının kareleri toplamına eşit olan sayılara \"kardeş sayılar\" denir.","Örnek olarak 13 = 2² + 3², 14 = 2² + 3² + 4², 29 = 2² + 3² + 4² + 5² şeklinde yazılmıştır.","35 sayısının ardışık iki veya üç pozitif tam sayının kareleri toplamı şeklinde yazılamadığı için kardeş sayı olmadığı belirtilmiştir."]},"beginTime":3281,"endTime":3365,"href":"/video/preview/6439299137845905469?parent-reqid=1769422724738290-1495271036736737050-balancer-l7leveler-kubr-yp-sas-261-BAL&text=marekd70&t=3281&ask_summarization=1"},{"index":25,"title":"Dersin Sonu ve Ödev","list":{"type":"unordered","items":["Dersin sonunda önemli sorular işaretlenmiştir: 4. soru, 7. örnek ve 3. örnek.","Yıldızlı soruların tekrar analiz edilmesi ve çözülmesi gerektiği vurgulanmıştır.","Ödev olarak TYT Matematik Soru Bankası'ndan ardışık sayılar temel tanım testi 1 ve 2'nin çözülmesi 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