Find a formula for the general term $a_{n}$ of the sequence, assuming that the pattern of the first few terms continues.

$\left\{4,-1, \frac{1}{4},-\frac{1}{16}, \frac{1}{64}, \ldots\right\}$

To find: A formula for the general term an of the sequence.

The formula for the general term an of the sequence is 4(−14)n−1 .

Given:

The first five terms of the given sequence are {4,−1,14,−116,134,...} .

Here, a1=4,a2=−1,a3=14,a4=−116 and a5=164 .

Calculation:

The first term of the given sequence is a1=4 .

The second term of the given sequence can be expressed as a2=4⋅(−14) .

The third term of the given sequence can be expressed as a3=4⋅(−14)2 .

The fourth term of the given sequence can be expressed as a4=4⋅(−14)3 .

The fifth term of the given sequence can be expressed as a5=4⋅(−14)4 .

Here, it is observed that the first term of the sequence is 4 and each term is −14 times the previous term.

Therefore, the formula for the general term an of the sequence is 4(−14)n−1 .