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

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

Answer»

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

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