Question

Find the n^th term of the series :

1, 2, 4, 8, ...............

Answer 1

Given series: 1, 2, 4, 8, ...............

Now,

`2/1 = 2, 4/2 = 2, 8/4 = 2`

Since `2/1 = 4/2 = 8/4 = ....... = 2,` the given sequence is a G.P. with first term, a = 1 and common ratio, r = 2.

Now, T_n = ar^{n – 1}

`\implies` T_n = 1 × 2^{n – 1}

= 2^{n – 1}