Question

Find the 10^th and nth term of G.P.: 5, 25, 125,…..

Answer 1

Given G.P.: 5, 25, 125,….. 

a = 5, r = \(\frac{a_2}{a_1}\) = \(\frac{25}{5}\)= 5 

a_n = a . r^n-1 = 5 × (5)^n-1 = 5^1+n-1 = 5ⁿ 

a₁₀ = a . r⁹ = 5 × 5⁹ = 5¹⁰ 

∴ a₁₀ = 5¹⁰; a_n = 5ⁿ