Question

Which term of the G. P. 5, 25, 125, 625, …… is 5¹⁰ ?

Answer 1

Here, t₁ = a = 5, r = \(\frac{t_2}{t_1}=\frac{25}5=5,t_n = 5^{10}\)

t_n = ar^n-1

\(\therefore\) 5¹⁰ = 5 x 5(n - 1)

\(\therefore\) 5¹⁰ = 5 x 5^(n-1)

\(\therefore\) 5¹⁰ = 5^{(1 + n - 1)}

\(\therefore\) 5¹⁰ = 5ⁿ 

\(\therefore\) n = 10

\(\therefore\) 5¹⁰ = 5ⁿ

\(\therefore\) n = 10

\(\therefore\) 5¹⁰ is the 10^th term of the G.P.

Alternate Method:

t₁ = 5, t₂ = 25 = 5², t₃ = 125 = 5³, t₄ = 625 = 5⁴

\(\therefore\) t₁₀ = 5¹⁰