Question

What is the sum of all even numbers 0-175 in algebraic form? If n49=99

Answer 1

`S_(88)=7656`

Explanation:

We want to find the sum of all even numbers from 0 to 175.

The series will be:

`0+2+4+6+...+174`

The explicit formula for this is
`a_n=2n-2`, where
`n\ge1`.

We need to find how many terms are there.

`2n-2=174`

`2n=176\\n=88`

The sum of terms is given by:

`S_n=(n)/(2)(a_1+l)`

Substitute n=88,
`a_1=0` and l=174 to get:

`S_(88)=(88)/(2)(0+174)\\S_(88)=44*174\\S_(88)=7656`