S8 = 5S4
r^8-1 = 5(r^4-1)
r^8 - 5r^4 + 4 = 0
r^4 = 1 or 4
r = ±1 or ±√2
Clearly r=±1 does not work. For r=√2, we have
1,√2,2,2√2,4,4√2,8,8√2
S4 = 3+3√2
S8 = 15+15√2
and similarly for -√2
The sum of the 8 terms of a GP is 5 times the sum of first 4 terms. Find the common ratio.
1 answer