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

$\left\{\frac{1}{2}, \frac{1}{4}, \frac{1}{6}, \frac{1}{8}, \frac{1}{10}, \ldots\right\}$

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

The formula for the general term an of the sequence is 12n .

Given:

The first five terms of the given sequence are {12,14,16,18,110,...} .

Here, a1=12 , a2=14 , a3=16 , a4=18 and a5=110 .

Calculation:

The first term of the given sequence can be expressed as a1=12⋅1 .

The second term of the given sequence can be expressed as a2=12⋅2 .

The third term of the given sequence can be expressed as a3=12⋅3 .

The fourth term of the given sequence can be expressed as a4=12⋅4 .

The fifth term of the given sequence can be expressed as a5=12⋅5 .

Here, the denominator is twice the number of the term n.

Therefore, the formula for the general term an of the sequence is 12n .