8. Sınıf Sayı Örüntüleri 2 Aritmetik ve Geometrik Dizi (TEOG) - Konu Anlatımı ve Soru Çözümleri
30,3bin30,3 bin izleme
Yayın tarihi 25 şub 201525 şub 2015
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İlk bölümde aritmetik diziler tanımlanarak ortak fark kavramı ve genel terim formülü (a_n = a_1 + (n-1)d) açıklanırken, ikinci bölümde geometrik diziler, ortak çarpan kavramı ve genel terim formülü (a_n = a_1 * r^(n-1)) örneklerle anlatılmaktadır.","Videoda her iki dizi türü için de formüller detaylı olarak açıklanmakta ve çeşitli örnekler çözülmektedir. Bu içerik, sayı örüntüleri konusunu öğrenmek veya pekiştirmek isteyenler için faydalı bir kaynaktır."]},"endTime":989,"title":"Sayı Örüntüleri: Aritmetik ve Geometrik Diziler","beginTime":0}],"fullResult":[{"index":0,"title":"Aritmetik Dizi","list":{"type":"unordered","items":["Aritmetik dizi, terimleri belirli bir kurala göre artan ya da azalan örüntülerdir.","Aritmetik dizilerde terimlerin azalış veya artış miktarlarına ortak fark denir.","Ortak fark artı veya eksi olabilir; artı ortak fark artan, eksi ortak fark azalan dizileri gösterir."]},"beginTime":0,"endTime":99,"href":"/video/preview/6684625352915435280?parent-reqid=1754513620822412-2212017074337779913-balancer-l7leveler-kubr-yp-sas-51-BAL&text=Taban%2BAritmeti%C4%9Fi%2B2%2B-%2BKonu%2BAnlat%C4%B1m%C4%B1%2Bve%2BSoru%2B%C3%87%C3%B6z%C3%BCmleri&t=0&ask_summarization=1"},{"index":1,"title":"Aritmetik Dizilerde Terim Bulma","list":{"type":"unordered","items":["Aritmetik dizide terimler arasındaki fark (ortak fark) biliniyorsa, sonraki terimler bulunabilir.","Aritmetik dizinin genel terimi a_n = a_1 + (n-1)r formülüyle hesaplanır.","Genel terim formülü kullanılarak belirli bir terim kolayca bulunabilir."]},"beginTime":99,"endTime":474,"href":"/video/preview/6684625352915435280?parent-reqid=1754513620822412-2212017074337779913-balancer-l7leveler-kubr-yp-sas-51-BAL&text=Taban%2BAritmeti%C4%9Fi%2B2%2B-%2BKonu%2BAnlat%C4%B1m%C4%B1%2Bve%2BSoru%2B%C3%87%C3%B6z%C3%BCmleri&t=99&ask_summarization=1"},{"index":2,"title":"Geometrik Dizi","list":{"type":"unordered","items":["Geometrik dizide terimler arasında belirli bir oran bulunur ve terimler birbirinin katı veya bölünmüş hali şeklinde gider.","Geometrik dizide kat şeklinde giden ifadelerde o kata ortak çarpan denir.","Ortak çarpan artı veya eksi olabilir; artı ortak çarpan artan, eksi ortak çarpan azalan dizileri gösterir."]},"beginTime":474,"endTime":580,"href":"/video/preview/6684625352915435280?parent-reqid=1754513620822412-2212017074337779913-balancer-l7leveler-kubr-yp-sas-51-BAL&text=Taban%2BAritmeti%C4%9Fi%2B2%2B-%2BKonu%2BAnlat%C4%B1m%C4%B1%2Bve%2BSoru%2B%C3%87%C3%B6z%C3%BCmleri&t=474&ask_summarization=1"},{"index":3,"title":"Geometrik Dizilerin Örnekleri","list":{"type":"unordered","items":["Geometrik dizilerde her terim belirli bir oranla (ortak çarpan) çarpılarak ilerler.","Geometrik dizinin terimleri küçülüyorsa, ortak çarpan 1'den küçük bir sayı olmalıdır.","Geometrik dizinin terimleri artıyorsa, ortak çarpan 1'den büyük bir sayı olmalıdır."]},"beginTime":588,"endTime":711,"href":"/video/preview/6684625352915435280?parent-reqid=1754513620822412-2212017074337779913-balancer-l7leveler-kubr-yp-sas-51-BAL&text=Taban%2BAritmeti%C4%9Fi%2B2%2B-%2BKonu%2BAnlat%C4%B1m%C4%B1%2Bve%2BSoru%2B%C3%87%C3%B6z%C3%BCmleri&t=588&ask_summarization=1"},{"index":4,"title":"Geometrik Dizinin Genel Terimi","list":{"type":"unordered","items":["Geometrik dizinin genel terimi (n. terim) formülü: a_n = a_1 × r^(n-1) şeklindedir.","İlk terimi 5, ortak çarpanı 3 olan geometrik dizinin dördüncü terimi 135'tir.","İlk terimi 64, ortak çarpanı 1/2 olan geometrik dizinin beşinci terimi 4'tür."]},"beginTime":711,"endTime":836,"href":"/video/preview/6684625352915435280?parent-reqid=1754513620822412-2212017074337779913-balancer-l7leveler-kubr-yp-sas-51-BAL&text=Taban%2BAritmeti%C4%9Fi%2B2%2B-%2BKonu%2BAnlat%C4%B1m%C4%B1%2Bve%2BSoru%2B%C3%87%C3%B6z%C3%BCmleri&t=711&ask_summarization=1"},{"index":5,"title":"Genel Terim Formülünün Uygulanması","list":{"type":"unordered","items":["İlk terimi 8, ortak çarpanı 1/2 olan geometrik dizinin genel terimi a_n = 2^(3-n) şeklindedir.","5, 10, 20, 40, 80 şeklinde giden geometrik dizinin ortak çarpanı 2'dir ve genel terimi a_n = 5 × 2^(n-1) şeklindedir."]},"beginTime":836,"endTime":988,"href":"/video/preview/6684625352915435280?parent-reqid=1754513620822412-2212017074337779913-balancer-l7leveler-kubr-yp-sas-51-BAL&text=Taban%2BAritmeti%C4%9Fi%2B2%2B-%2BKonu%2BAnlat%C4%B1m%C4%B1%2Bve%2BSoru%2B%C3%87%C3%B6z%C3%BCmleri&t=836&ask_summarization=1"}],"linkTemplate":"/video/preview/6684625352915435280?parent-reqid=1754513620822412-2212017074337779913-balancer-l7leveler-kubr-yp-sas-51-BAL&text=Taban%2BAritmeti%C4%9Fi%2B2%2B-%2BKonu%2BAnlat%C4%B1m%C4%B1%2Bve%2BSoru%2B%C3%87%C3%B6z%C3%BCmleri&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"8. 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İlk bölümde aritmetik diziler tanımlanarak ortak fark kavramı ve genel terim formülü (a_n = a_1 + (n-1)d) açıklanırken, ikinci bölümde geometrik diziler, ortak çarpan kavramı ve genel terim formülü (a_n = a_1 * r^(n-1)) örneklerle anlatılmaktadır.","Videoda her iki dizi türü için de formüller detaylı olarak açıklanmakta ve çeşitli örnekler çözülmektedir. Bu içerik, sayı örüntüleri konusunu öğrenmek veya pekiştirmek isteyenler için faydalı bir kaynaktır."]},"endTime":989,"title":"Sayı Örüntüleri: Aritmetik ve Geometrik Diziler","beginTime":0}],"fullResult":[{"index":0,"title":"Aritmetik Dizi","list":{"type":"unordered","items":["Aritmetik dizi, terimleri belirli bir kurala göre artan ya da azalan örüntülerdir.","Aritmetik dizilerde terimlerin azalış veya artış miktarlarına ortak fark denir.","Ortak fark artı veya eksi olabilir; artı ortak fark artan, eksi ortak fark azalan dizileri gösterir."]},"beginTime":0,"endTime":99,"href":"/video/preview/6684625352915435280?parent-reqid=1754513620822412-2212017074337779913-balancer-l7leveler-kubr-yp-sas-51-BAL&text=Taban%2BAritmeti%C4%9Fi%2B2%2B-%2BKonu%2BAnlat%C4%B1m%C4%B1%2Bve%2BSoru%2B%C3%87%C3%B6z%C3%BCmleri&t=0&ask_summarization=1"},{"index":1,"title":"Aritmetik Dizilerde Terim Bulma","list":{"type":"unordered","items":["Aritmetik dizide terimler arasındaki fark (ortak fark) biliniyorsa, sonraki terimler bulunabilir.","Aritmetik dizinin genel terimi a_n = a_1 + (n-1)r formülüyle hesaplanır.","Genel terim formülü kullanılarak belirli bir terim kolayca bulunabilir."]},"beginTime":99,"endTime":474,"href":"/video/preview/6684625352915435280?parent-reqid=1754513620822412-2212017074337779913-balancer-l7leveler-kubr-yp-sas-51-BAL&text=Taban%2BAritmeti%C4%9Fi%2B2%2B-%2BKonu%2BAnlat%C4%B1m%C4%B1%2Bve%2BSoru%2B%C3%87%C3%B6z%C3%BCmleri&t=99&ask_summarization=1"},{"index":2,"title":"Geometrik Dizi","list":{"type":"unordered","items":["Geometrik dizide terimler arasında belirli bir oran bulunur ve terimler birbirinin katı veya bölünmüş hali şeklinde gider.","Geometrik dizide kat şeklinde giden ifadelerde o kata ortak çarpan denir.","Ortak çarpan artı veya eksi olabilir; artı ortak çarpan artan, eksi ortak çarpan azalan dizileri gösterir."]},"beginTime":474,"endTime":580,"href":"/video/preview/6684625352915435280?parent-reqid=1754513620822412-2212017074337779913-balancer-l7leveler-kubr-yp-sas-51-BAL&text=Taban%2BAritmeti%C4%9Fi%2B2%2B-%2BKonu%2BAnlat%C4%B1m%C4%B1%2Bve%2BSoru%2B%C3%87%C3%B6z%C3%BCmleri&t=474&ask_summarization=1"},{"index":3,"title":"Geometrik Dizilerin Örnekleri","list":{"type":"unordered","items":["Geometrik dizilerde her terim belirli bir oranla (ortak çarpan) çarpılarak ilerler.","Geometrik dizinin terimleri küçülüyorsa, ortak çarpan 1'den küçük bir sayı olmalıdır.","Geometrik dizinin terimleri artıyorsa, ortak çarpan 1'den büyük bir sayı olmalıdır."]},"beginTime":588,"endTime":711,"href":"/video/preview/6684625352915435280?parent-reqid=1754513620822412-2212017074337779913-balancer-l7leveler-kubr-yp-sas-51-BAL&text=Taban%2BAritmeti%C4%9Fi%2B2%2B-%2BKonu%2BAnlat%C4%B1m%C4%B1%2Bve%2BSoru%2B%C3%87%C3%B6z%C3%BCmleri&t=588&ask_summarization=1"},{"index":4,"title":"Geometrik Dizinin Genel Terimi","list":{"type":"unordered","items":["Geometrik dizinin genel terimi (n. terim) formülü: a_n = a_1 × r^(n-1) şeklindedir.","İlk terimi 5, ortak çarpanı 3 olan geometrik dizinin dördüncü terimi 135'tir.","İlk terimi 64, ortak çarpanı 1/2 olan geometrik dizinin beşinci terimi 4'tür."]},"beginTime":711,"endTime":836,"href":"/video/preview/6684625352915435280?parent-reqid=1754513620822412-2212017074337779913-balancer-l7leveler-kubr-yp-sas-51-BAL&text=Taban%2BAritmeti%C4%9Fi%2B2%2B-%2BKonu%2BAnlat%C4%B1m%C4%B1%2Bve%2BSoru%2B%C3%87%C3%B6z%C3%BCmleri&t=711&ask_summarization=1"},{"index":5,"title":"Genel Terim Formülünün Uygulanması","list":{"type":"unordered","items":["İlk terimi 8, ortak çarpanı 1/2 olan geometrik dizinin genel terimi a_n = 2^(3-n) şeklindedir.","5, 10, 20, 40, 80 şeklinde giden geometrik dizinin ortak çarpanı 2'dir ve genel terimi a_n = 5 × 2^(n-1) şeklindedir."]},"beginTime":836,"endTime":988,"href":"/video/preview/6684625352915435280?parent-reqid=1754513620822412-2212017074337779913-balancer-l7leveler-kubr-yp-sas-51-BAL&text=Taban%2BAritmeti%C4%9Fi%2B2%2B-%2BKonu%2BAnlat%C4%B1m%C4%B1%2Bve%2BSoru%2B%C3%87%C3%B6z%C3%BCmleri&t=836&ask_summarization=1"}],"linkTemplate":"/video/preview/6684625352915435280?parent-reqid=1754513620822412-2212017074337779913-balancer-l7leveler-kubr-yp-sas-51-BAL&text=Taban%2BAritmeti%C4%9Fi%2B2%2B-%2BKonu%2BAnlat%C4%B1m%C4%B1%2Bve%2BSoru%2B%C3%87%C3%B6z%C3%BCmleri&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"8. 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