{ \(a_n\)} is a geometric sequence with common ratio r > 0. If \(a_1\)= 1, \(6a_n\)= \(a_{n+1}+a_{n+2}\), then find the sum of the first 4 terms of { \(a_n\)} .
a = 1
6a = a2 + a3
6 = a2 +a3
6 = ar + ar^2
6 = 1r + 1r^2
6 = r + r^2
r^2 + r - 6 = 0
(r - 2) ( r + 3) = 0
r - 2 = 0
r = 2
So
S4 = 1 + 2 + 2^2 + 2^3 = 15
Thanks so much CPhill, you are a really good answerer
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