Find a formula for the general term $a_{n}$ of the sequence, assuming that the pattern of the first few terms continues.$\{5,8,11,14,17, \ldots\}$

To find: Formula for general term an of the sequence.

The formula for general term an of the sequence is 2+3n_ .

Given:

The sequence is {5,8,11,14,17,...} .

Here, a1=3,a2=5,a3=8,a4=14 and a5=17

Calculation:

The first term of the sequence can be expressed as follows:

a1=2+3 =2+3⋅1

The second term of the sequence can be expressed as follows:

a2=2+6 =2+3⋅2

The third term of the sequence can be expressed as follows:

a3=2+9 =2+3⋅3

The fourth term of the sequence can be expressed as follows:

a4=2+12 =2+3⋅4

The fifth term of the sequence can be expressed as follows:

a5=2+15 =2+3⋅5

Here, it is observed that every term is greater than the previous term by 3.

Therefore, the formula for general term an of the sequence is 2+3n .