Question

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.​

Answer 1

a=1

3rd term=ar^2

5th term=ar^4

3rd +5th=ar^2(1+ar^2)=90

r^4+r^2-90=0

r^2=x

x^2+x-90=0

solving eq x=10,-9

r=+(10)^1/2

r=-(10)^1/2

Answer 2

➠Question:-

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.

➠Solution:-

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The first term of the given Geometric Progression a = 1.

Let ‘r’ be the common ratio of the Geometric Progression.

According to the problem,

⇒t3 + t5 = 90

⇒ar² + ar⁴ = 90

⇒r²+ r⁴ = 90

⇒r⁴ + r² – 90 = 0

⇒r² + 10r² - 9r² - 90 = 0

⇒(r² + 10)(r² - 9) =0

⇒r² - 9 = 0

⇒r² = 9

⇒r = ±3

Therefore, the common ratio of the Geometric Progression is -3 or 3.

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