Question

Write the explicit formula for the sequence below and use it to find the 47th term:

-3, 5, 13, 21, . . .

Answer 1

Given:

The sequence is:

`-3,5,13,21...`

To find:

The explicit formula for the given sequence then find the 47th term.

Solution:

We have,

`-3,5,13,21...`

The difference between two consecutive terms are:

`5-(-3)=8`

`13-5=8`

`21-13=8`

The given sequence has a common difference. So, the given sequence is an arithmetic sequence with first term -3 and common difference 8.

The explicit formula for an arithmetic sequence is:

`a_n=a+(n-1)d`

Where, a is the first term and d is the common difference.

Putting
`a=-3` and
`d=8` in the above formula, we get

`a_n=-3+(n-1)8`

`a_n=-3+8n-8`

`a_n=8n-11`

Putting
`n=47`, we get

`a_(47)=8(47)-11`

`a_(47)=376-11`

`a_(47)=365`

Therefore, the explicit formula for the given sequence is
`a_n=8n-11` and the 47th term is 365.