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.