Question

Tentukan banyak suku dari barisan berikut!
6+9+12+15+...=756
56+51+46+41+...=-36
10+14+18+22+...=640

Answer 1

1) Sn = n/2(2a +(n-1)b)
756 = n/2(2(6) + (n-1)3)
756 x 2 = n (12+ 3n -3)
1512 = n ( 3n + 9)
1512 = 3n^2 + 9n
n^2 + 3n = 504
n^2 + 3n - 504 = 0
(n+24)(n-21) = 0
n = -24 tidak memenuhi
n = 21

2) rumus sama dg no 1
-36 = n/2(2(56) + (n-1)(-5)
-36 x 2 = n(112 - 5n + 5)
-72 = n ( -5n + 117)
5n^2 - 117n - 72 = 0
(5n+3)(n-24) = 0
5n+3 = 0 tdk memenuhi
n-24 = 0
n = 24

3) rumus tetap sama
640 = n/2 (2(10) +(n-1)4)
640 x 2 = n(20+4n-4)
1280 = n(4n+16)
4n^2 + 16n - 1280 = 0
n^2 + 4n - 320 = 0
(n+20)(n-16) = 0
n+20 = 0 tdk memenuhi
n-16 = 0
n = 16