Question

Find the 9^th term of the series :

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

Answer 1

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

Now,

${\displaystyle \frac{4}{1}=4,\frac{16}{4}=4,\frac{64}{16}=4}$

Since ${\displaystyle \frac{4}{1}=\frac{16}{4}=\frac{64}{16}=......=4,}$ the given sequence is a G.P. with the first term, a = 1 and common ratio, r = 4.

Now, T_n = ar^{n – 1}

${\displaystyle \Rightarrow }$ T₉ = 1 × 4^{9 – 1} 

= 1 × 4⁸

= 4⁸

= 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4

= 65536