MHB ACT Problem: Sum Of Even Integers

[816318]

What is the sum of all the even integers between 1 and 101? Is there an easier way besides using the formula: (B-A+1)(B+A)/2?

It just takes too much time.

 

[Greg]

Re: ACT problem

It's an arithmetic series with first term 2 and fifty terms, so it can easily be calculated as

$$\frac{n}{2}[2a_1+(n-1)d]$$

with $n$ (the number of terms) = $50$, $a_1$ (the first term) = $2$ and $d$ (the common difference) = $2$.

Alternatively, use

$$\frac{n(a_1+a_n)}{2}$$

with $a_n$ being the last term ($100$).

 

[MarkFL]

Re: ACT problem

Another approach would be:

$$S=2\sum_{k=1}^{50}(k)=50\cdot51$$