Menemukan Nilai Suku Tengah dalam Barisan Geometri
Dalam matematika, barisan geometri adalah urutan bilangan di mana setiap suku diperoleh dengan mengalikan suku sebelumnya dengan suatu bilangan tetap yang disebut rasio. Dalam artikel ini, kita akan mencari nilai suku tengah dari dua barisan geometri yang berbeda. a. Barisan Geometri 2, 6, 18, ..., 1.458 Untuk mencari nilai suku tengah dari barisan geometri ini, kita perlu mengetahui rasio antara suku-suku yang berdekatan. Dalam hal ini, rasio antara suku-suku adalah 6/2 = 3. Dengan mengetahui rasio ini, kita dapat menggunakan rumus umum untuk mencari suku tengah dalam barisan geometri. Rumus umum untuk mencari suku tengah dalam barisan geometri adalah sebagai berikut: \( a_n = a_1 \times r^{(n-1)} \) Di sini, \( a_n \) adalah suku ke-n dalam barisan, \( a_1 \) adalah suku pertama dalam barisan, r adalah rasio antara suku-suku, dan n adalah jumlah suku dalam barisan. Dalam kasus ini, kita ingin mencari suku tengah, yang berarti kita ingin mencari suku ke-n/2. Jadi, kita dapat menggunakan rumus ini untuk mencari suku tengah dalam barisan ini. \( a_{n/2} = a_1 \times r^{(n/2-1)} \) Dalam kasus ini, suku pertama \( a_1 \) adalah 2, rasio r adalah 3, dan jumlah suku n adalah 5 (karena kita memiliki 5 suku dalam barisan). 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