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

Answer:

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

Step-by-step 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

$S_n=\frac{n}{2}[2a+(n-1)d]$

$S_{13}=\frac{13}{2}[2(6)+(13-1)(3)]$

$S_{13}=\frac{13}{2}[12+36]$

$S_{13}=312$

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