Question

Find the sum of all the integers from $1$ to $1000$

• A. 5050
• B. 50500
• C. 500500
• D. 50050

Answer 1

The correct option is C 500500

The sequence of integers starting from $1$ to $1000$ is given by

$1,2,3,4,...,1000$

The above sequence has $1000$ terms. The first term is $1$ and the last term is $1000$ and the common difference is equal to $1$.

We have the formula that gives the sum of the first $n$ terms of an arithmetic sequence knowing the first and last term of the sequence and the number of terms (see formula above).

$s_{1000}=\frac{1000(1+1000)}{2}=500500$