Question

Find the 9^th term of the series :

1, 4, 16, 64, ...............

Answer 1

Given sequence: 1, 4, 16, 64, ...............

Now,

`4/1 = 4, 16/4 = 4, 64/16 = 4`

Since `4/1 = 16/4 = 64/16 = ...... = 4,` the given sequence is a G.P. with the first term, a = 1 and common ratio, r = 4.

Now, T_n = ar^{n – 1}

`\implies` T₉ = 1 × 4^{9 – 1} 

= 1 × 4⁸

= 4⁸

= 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4

= 65536