Question

What is the sum of the arithmetic sequence 8, 15, 22 …, if there are 26 terms?

Answer 1

`2483`

Explanation:

To calculate the `color(blue)"sum of n terms"` for an arithmetic sequence.

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(S_n=n/2[2a+(n-1)d])color(white)(a/a)|)))`
where a represents the first term and d, the common difference.

here a = 8, d = 22 - 15 = 15 - 8 = 7 and n = 26

`rArrS_(26)=26/2[(2xx8)+(25xx7)]`

`=13(16+175)=2483`