Question

Find the sum of a finite arithmetic sequence from n = 1 to n = 13, using the expression 3n + 3.

Answer 1

The sum of an arithmetic sequence is the average of the first and last terms time the number of terms...

So the first term is 3+3 and the last term is 3(13)+3

So the sum is:

13(6+42)/2

312

Answer 2

The sum of a finite arithmetic sequence from n = 1 to n = 13 is 312.

Explanation:

The given expression is

`3n+3`

For n=1,

`3(1)+3=6`

For n=2,

`3(2)+3=9`

For n=3,

`3(3)+3=12`

The required AP is

`6, 9, 12, ...`

Here first term is 6 and common difference is 3.

The sum of n terms of an AP is

`S_n=(n)/(2)[2a+(n-1)d]`

`S_(13)=(13)/(2)[2(6)+(13-1)(3)]`

`S_(13)=(13)/(2)[12+36]`

`S_(13)=312`

Therefore the sum of a finite arithmetic sequence from n = 1 to n = 13 is 312.