Question

How do you find the sum of the arithmetic sequence (x+y)+(x+2y)+...+(x+10y)?

Answer 1

`5(2x+11y)`.

Explanation:

In the Usual Notation, we have,

`a=x+y, d=(x+2y)-(x+y)=y, n=10, &,`

`l"=the last term="x+10y`.

`:. S_10=n/2[a+l]`,

`=10/2[(x+y)+(x+10y)]`.

`rArr S_10=5(2x+11y)`.