Find the 12th term of a GP with common ratio 2, whose 8th term is 192. Class 9

Find the 12^th term of a GP with common ratio 2, whose 8^th term is 192. Class 9

Question 1.

Find the 12^th term of a GP with common ratio 2, whose 8^th term is 192. Class 9

Solution:

Given, r = 2, t₈ = 192

t_n = ar^n-1

∴ t₈ = a × 2⁷

∴ 192 = a × 128

∴ a = $\frac{192}{128}$

∴ a = $\frac{3}{2}$

Now, for n = 12

t₁₂ = ar¹¹

∴ t₁₂ = $\frac{3}{2}$ x 2¹¹

∴ t₁₂ = 3 × 2¹⁰

∴ t₁₂ = 3 × 1024

∴ t₁₂ = 3072

∴ 12^th term of a GP is 3072.

Question 2.

Find the 10^th and n^th terms of the GP: 5, 25, 125,.... Class 9

Solution:

Here,

a = 5, r $=\frac{t_2}{t_1}=\frac{25}{5}=5$

t_n = ar^n-1

= 5 × 5^n-1

= 5^(1+n-1) = 5ⁿ

For n = 10,

t₁₀ = 5¹⁰

∴ 5¹⁰ and 5ⁿ are the 10^th and n^th terms of the GP, respectively.