Question

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

Answer 1

Answer:

$S_{88}=7656$

Step-by-step 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:

$S_n=\frac{n}{2}(a_1+l)$

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

$S_{88}=\frac{88}{2}(0+174)\\S_{88}=44*174\\S_{88}=7656$