Question

Question 9 The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

Class X1 - Maths -Sequences and Series Page 199

Answer 1

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Answer 2

Let the GP is a , ar , ar² , ar³ , ......... arⁿ⁻¹
Here,
first term ( a ) = 1
and 3rd term ( T₃ ) + 5th term ( T₅ ) = 90
e.g T₃ + T₅ = 90

use formula,
T = arⁿ⁻¹
T₃ = 1.( r )³⁻¹ = r²
T₅ = 1.( r )⁵⁻¹ = r⁴
Therefore, r² + r⁴ = 90
r⁴ + r² - 90 = 0
r⁴ + 10r² - 9r² - 90 = 0
r²( r² + 10) - 9( r² + 10) = 0
(r² + 10)(r² - 9) = 0
r² + 10 ≠ 0 so, r² - 9 = 0
r = ±3