Question

1; 4; 16; 64; ...what is the general term ​

Answer 1

Given:

The sequence is

1, 4, 16, 64

To find:

The general term of the given sequence.

Solution:

We have, the sequence

1, 4, 16, 64

Here, the ratio between two consecutive terms is same. So, it is a geometric sequence.

First term is:

$a=1$

Common ratio is:

$r=\dfrac{a_2}{a_1}$

$r=\dfrac{4}{1}$

$r=4$

The nth term of a geometric sequence is

$a_n=ar^{n-1}$             ...(i)

Where, a is the first term and r is the common ratio.

Putting a=1 and r=4 in (i), we get

$a_n=(1)(4)^{n-1}$

$a_n=4^{n-1}$

Therefore, the general term of the given sequence is $a_n=4^{n-1}$.