Tentukan n jika: 1. 1 + 2 + 3 + ……….. + n = 120 2. 5 + 7 + 9 + ……….. + n = 192

nomor 1. 194/ nomor 2. 171 maaf ya kalau salah

1) 1 + 2 + 3 + .... + n = 120 => a = 1, b = 2 - 1 = 1
Sn = 120
n/2 (2a + (n - 1)b) = 120
n/2 (2(1) + (n - 1)(1)) = 120
n/2 (2 + n - 1) = 120
n/2 (n + 1) = 120 ===> kali 2
n(n + 1) = 240
n^2 + n - 240 = 0
(n + 16)(n - 15) = 0
n = -16 atau n = 15
Yang diambil yg positif : n = 15
n di soal adalah suku ke 15
n = U15 = a + 14b = 1 + 14(1) = 15 => jawaban

2) 5 + 7 + 9 + .... + n = 192 => a = 5, b = 7 - 5 = 2
Sn = 192
n/2 (2a + (n - 1)b) = 192
n/2 (2(5) + (n - 1)2) = 192
n/2 (10 + 2n - 2) = 192
n/2 (2n + 8) = 192
n^2 + 4n - 192 = 0
(n + 16)(n - 12) = 0
n = -16 atau n = 12
Ambil yang positif => n = 12
n di soal adalah suku ke 12
n = U12 = a + 11b = 5 + 11(2) = 27 => jawaban