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For Our Book Sales: https://www.benimhocam.com / benimhocamyayin / benimhocam / benimhocamyayin...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3226426/69e59458a15ecbeb4a6f0bea9841afd6/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/kbxCIQIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"16","reqid":"1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL&text=videoid:15231787610835900843","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin ardışık sayılar konusunu anlattığı eğitim içeriğidir. Öğretmen, \"Usta\" ve \"Gavs amca\" olarak hitap ettiği matematikçiler hakkında da bilgi vermektedir.","Video, ardışık sayıların tanımı, özellikleri ve toplam formülleri üzerine odaklanmaktadır. Öğretmen önce ardışık sayıların tanımını yaparak, ardışık tek sayılar ve ardışık çift sayılar arasındaki farkları anlatır, ardından ardışık sayıların toplam formüllerini detaylı olarak açıklar ve örnek sorular çözer. Ayrıca Gauss'un 1'den 100'e kadar olan sayıları toplama formülünü nasıl bulduğunu anlatan bir hikaye paylaşır.","Videoda formüllerin ezberlenmesi yerine mantığının anlaşılmasının önemi vurgulanmakta ve ardışık sayılarla ilgili denklem sorularının çözüm teknikleri gösterilmektedir. Öğretmen, KPSS gibi sınavlarda sorulmayacak ancak konuyu pekiştirmek için alıştırmalar yapılacağını belirtmektedir."]},"endTime":2087,"title":"Ardışık Sayılar Matematik Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Ardışık Sayılar Kavramı","list":{"type":"unordered","items":["Ardışık sayılar, sayısal mantığın altyapısını oluşturan ve ilerde birçok konuda sıkça kullanılacak önemli bir konudur.","Ardışık sayılar, aralarındaki farkı bir olan sayılardır; örneğin 2, 3, 4 veya -1, -2, -3 şeklinde giden sayılar.","Ardışık sayılar için a ve b sayıları arasında a-b=1 veya a-b=-1 ilişkisi vardır."]},"beginTime":3,"endTime":144,"href":"/video/preview/15231787610835900843?parent-reqid=1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL&text=KGS&t=3&ask_summarization=1"},{"index":1,"title":"Ardışık Tek ve Çift Sayılar","list":{"type":"unordered","items":["Ardışık tek sayılar, aralarındaki farkı iki olan sayılardır; örneğin 1, 3, 5, 7 veya n, n+2, n+4 şeklinde gider.","Ardışık çift sayılar da aralarındaki farkı iki olan sayılardır; örneğin 2, 4, 6, 8 veya n, n+2, n+4 şeklinde gider.","Ardışık tek ve çift sayılar genellikle EBOB-EKOK sorularında kullanılır."]},"beginTime":144,"endTime":336,"href":"/video/preview/15231787610835900843?parent-reqid=1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL&text=KGS&t=144&ask_summarization=1"},{"index":2,"title":"Ardışık Sayılarla İlgili Soru Çözüm Teknikleri","list":{"type":"unordered","items":["Ardışık sayılarla ilgili, eşitlik olmadığı ve değer sorulduğunda, uygun değerler vererek soruyu çözmek gerekir.","Ardışık sayılarla ilgili sorularda, aralarındaki farkı bir olarak eşitlik kurmak gerekir; örneğin 2n+1 ve n-3 ardışık sayılar ise 2n+1-(n-3)=1 veya 2n+1-(n-3)=-1 şeklinde eşitlik kurulur.","Ardışık sayılarla ilgili sorularda, hangisinin büyük olduğunu bilmediğimiz için iki durumda işlem yapmak gerekir."]},"beginTime":336,"endTime":650,"href":"/video/preview/15231787610835900843?parent-reqid=1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL&text=KGS&t=336&ask_summarization=1"},{"index":3,"title":"Ardışık Sayılar Problemi Çözümü","list":{"type":"unordered","items":["Ardışık sayılar problemlerinde, denklem verildiğinde ardışık sayıları (x, y, z) n, n+1, n+2 şeklinde veya x, x+1, x+2 şeklinde yazmak daha doğru ve hata yapmamak için daha iyi bir yöntemdir.","Verilen denklem 2x = 6xz - x - y şeklindeyken, ardışık sayılar yerine konulduğunda n = -6 bulunur.","Ardışık sayılar -6, -5, -4 olduğundan x+z toplamı -6 + (-4) = -10 olarak hesaplanır."]},"beginTime":653,"endTime":845,"href":"/video/preview/15231787610835900843?parent-reqid=1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL&text=KGS&t=653&ask_summarization=1"},{"index":4,"title":"Ardışık Sayılar Problemi Çözümü 2","list":{"type":"unordered","items":["ABC ardışık sayılar ve 1/a - 1/b - 1/c = 4/5 olduğunda, ardışık sayıları a=n, b=n+1, c=n+2 şeklinde yazarak denklem kurulur.","Denklem çözüldüğünde n = 13 bulunur, dolayısıyla a=13, b=14, c=15 olur.","a+b+c toplamı 13+14+15 = 42 olarak hesaplanır."]},"beginTime":845,"endTime":1033,"href":"/video/preview/15231787610835900843?parent-reqid=1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL&text=KGS&t=845&ask_summarization=1"},{"index":5,"title":"Gauss'un Ardışık Sayılar Formülü","list":{"type":"unordered","items":["Gauss, matematiğin prensi olarak bilinen önemli bir matematikçidir.","Gauss, 1'den 100'e kadar sayıların toplamını bulmak için 1+2+3+...+100 ve 100+99+98+...+1 şeklinde iki satır yazıp taraf tarafa topladı.","Her toplamın 101 olduğu ve 100 tane 101 olduğu görüldüğünde, toplamın 100×101/2 olduğu sonucuna vardı.","Bu formül, 1'den n'e kadar ardışık sayıların toplamı için n×(n+1)/2 formülüne dayanır."]},"beginTime":1033,"endTime":1250,"href":"/video/preview/15231787610835900843?parent-reqid=1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL&text=KGS&t=1033&ask_summarization=1"},{"index":6,"title":"Karesel Sayılar ve Formülleri","list":{"type":"unordered","items":["Ardışık tek sayıları topladığımızda karesel sayılar elde edilir: 1+3=4 (2²), 1+3+5=9 (3²), 1+3+5+7=16 (4²).","Karesel sayıların formülü, ilk ve son sayının toplamının yarısının karesi olarak hesaplanır.","Eğer formül birden başlamazsa, birden başlıyormuş gibi düşünüp eksik olan parçayı geri çıkarmak gerekir."]},"beginTime":1312,"endTime":1454,"href":"/video/preview/15231787610835900843?parent-reqid=1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL&text=KGS&t=1312&ask_summarization=1"},{"index":7,"title":"Genel Toplam Formülü","list":{"type":"unordered","items":["Genel toplam formülü, ortadaki sayı çarpı terim sayısı şeklinde ifade edilir.","Terim sayısı, son terim eksi ilk terim bölü ortak fark artı bir şeklinde hesaplanır.","Ortadaki sayı, ilk ve son terimin toplamının yarısıdır."]},"beginTime":1454,"endTime":1752,"href":"/video/preview/15231787610835900843?parent-reqid=1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL&text=KGS&t=1454&ask_summarization=1"},{"index":8,"title":"Formüllerin Uygulanması","list":{"type":"unordered","items":["Ardışık sayıların toplamı için özel formül kullanılabilir: n(n+1)/2.","Genel toplam formülü de kullanılabilir: ortadaki sayı çarpı terim sayısı.","Her iki formül de aynı sonucu verir ve pratik olarak hesaplanabilir."]},"beginTime":1752,"endTime":1853,"href":"/video/preview/15231787610835900843?parent-reqid=1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL&text=KGS&t=1752&ask_summarization=1"},{"index":9,"title":"Ardışık Sayılar Problemi","list":{"type":"unordered","items":["Ardışık beş doğal sayının toplamı yetmişbeş ise bu sayıların en küçüğü kaçtır sorusu çözülecek.","Bu tür sorular genellikle sınavlarda sorulmaz, ancak alıştırma amaçlı çözülür."]},"beginTime":1857,"endTime":1879,"href":"/video/preview/15231787610835900843?parent-reqid=1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL&text=KGS&t=1857&ask_summarization=1"},{"index":10,"title":"İlk Çözüm Yöntemi","list":{"type":"unordered","items":["İlk yöntemde ardışık sayılar n, n+1, n+2, n+3, n+4 şeklinde gösterilir ve toplamları 75'e eşitlenir.","Denklem çözülür: 5n + 10 = 75, n = 13 bulunur.","Sayılar 13, 14, 15, 16, 17 olur ve en küçüğü 13'tür."]},"beginTime":1879,"endTime":1984,"href":"/video/preview/15231787610835900843?parent-reqid=1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL&text=KGS&t=1879&ask_summarization=1"},{"index":11,"title":"Özel Çözüm Yöntemi","list":{"type":"unordered","items":["Özel yöntemde toplam = orta sayı × terim sayısı formülü kullanılır.","Orta sayı = toplam ÷ terim sayısı = 75 ÷ 5 = 15 bulunur.","Orta sayı 15 olduğunda, ardışık sayılar 13, 14, 15, 16, 17 olur ve en küçüğü 13'tür."]},"beginTime":1984,"endTime":2046,"href":"/video/preview/15231787610835900843?parent-reqid=1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL&text=KGS&t=1984&ask_summarization=1"},{"index":12,"title":"Sonuç","list":{"type":"unordered","items":["Bu tür sorular sadece olayı anlamak ve pekiştirmek için çözülür, KPSS'de böyle sorular sormaz.","İki çözüm yöntemi vardır: denklem kurma veya orta sayıyı bulma."]},"beginTime":2046,"endTime":2083,"href":"/video/preview/15231787610835900843?parent-reqid=1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL&text=KGS&t=2046&ask_summarization=1"}],"linkTemplate":"/video/preview/15231787610835900843?parent-reqid=1769248597972333-17997355884990361596-balancer-l7leveler-kubr-yp-sas-224-BAL&text=KGS&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"12) KPSS Mathematics - 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İlk bölümde teknoloji çağından bahsedilerek, kaynak toplama için el koyma emri kullanımı ve kaynak pazarından hızlı kaynak elde etme yöntemleri anlatılmaktadır. İkinci bölümde ise kışla sistemi ve birim ağacı üzerinden kaynak toplama artışı sağlayan birimler (oduncular, serfler, köy bekçileri) tanıtılmaktadır. 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