Math, asked by kushal95gdu, 1 year ago

the first term of a G.P. is 1. the sum of third and fifth terms is 90. find the common ratio of the G.P.

Answers

Answered by Aditiagrawal8
18

a1= 1

a3 + a5 = 90

a3= a1*r^2 = r^2

a5 = a1 *r^4 = r^4

=r^2 + r^4 = 90

= r^4 + r^2 - 90 =0

= (r^2 + 10) (r^2 - 9) = 0

= (r^2 + 10) ( r-3)(r+3) = 0

r=+3,-3

Answered by IshanS
11
Hi there!

a_1, a_2, a_3, ..... is a Geoometric progression.

Given,

a_1 = 1

a_3 + a_5 = 90

But_

a_3 = a_1 r² = r²

a_5 = a_1 r⁴ = r⁴

r² + r⁴ = 90

r⁴ + r⁴ - 90 = 0

(r2 + 10) (r² - 9) = 0

(r² + 10) ( r - 3)(r + 3) = 0

Thus,

r_1 = 3

r_2 = -3

Hope it helps! :D

Cheers,
Ishaan Singh

Anonymous: wrong and copied
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