Question

Write an explicit formula for an, the nth term of the sequence 5, 15, 25, ....

Answer 1

Given:

The sequence is 5, 15, 25, ... .

To find:

The explicit formula for the nth term of the given sequence.

Solution:

We have,

5, 15, 25, ...

It is an AP because the difference between two consecutive terms are same.

Here,

First term : a = 5

Common difference : d = 15 - 5 = 10

Now, the explicit formula for the nth term of an AP is

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

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

$a_n=5+(n-1)10$

$a_n=5+10n-10$

$a_n=10n-5$

Therefore, the required explicit formula for the given sequence is $a_n=10n-5$.