Question

In a G.P, the product of the 2nd and 4th term is double the 5th term, and the sum of first 4th term is 80. Find the G.P

Answer 1

term 2 = a r
term 4 = a r^3

term 5 = a r^4

term 1 = 1
term 3 = a r^2

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ar (ar^3) = 2 (a r^4)
a^2 r^4 = 2 a r^4
2 a = a^2
a^2 - 2 a = 0
a = 0 (won't work)
or
a = 2
now we need r
I assume you mean the sum of the first 4 is 80
a + ar + ar^2 + a r^3 = 80
1 + r + r^2 + r^3 = 40
r^3 + r^2 + r - 39 = 0
if r = 3
27 + 9 + 3 - 39 = 39-39 = 0 whew
so
2 *3^(n-1)

Answer 2

Pls n indicates