Question

Bila k-2, 2k+1, dan 6k+3 merupakan barisan geometri maka nilai k adalah

Answer 1

R = U2/U1 = 2k+1/k-2
r = U3/U2 = 6k+3/2k+1

2k+1/k-2 = 6k+3/2k+1
(2k+1)(2k+1) = (k-2)(6k+3)
4k^2 +2k +2k +1 = 6k^2+ 3k - 12k -6
2k^2 -13k -7 = 0
(2k +1) (k - 7) = 0
2k +1 = 0 atau k-7 = 0
2k  = -1             k = 7
k = -1/2

jika k= -1/2 -> -2 1/2, 0, 0 (tdk memenuhi)
jika k= 7 ->  5, 15, 45 (memenuhi dg r = 3)
jadi k = 7