Question

Find the 4th and 9th terms of the G.P. with first term 4 and common ratio 2.

Answer 1

In the given G.P., we have the first term, i.e, a = 4, and the common ratio, i.e., r = 2.
We know that the n^th term of the G.P. is t_n = ar^{n – 1}.
By taking a = 4, r = 2 and n = 4, we get:
t₄ = (4)(2)^{4 – 1}
$\Rightarrow$t₄ = (4)(2)³ = 4 × 8 = 32
Now,
By taking a = 4, r = 2 and n = 9, we get:
t₉ = (4)(2)^{9 – 1}
$\Rightarrow$t₉ = (4)(2)⁸
$\Rightarrow$t₉ = 4 × 256 = 1024
Thus, the 4^th term is 32 and the 9^th term is 1024.