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=(a_2)/(a_1)`

`r=(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)`.