# What two consecutive numbers are equal to 100?

Jun 6, 2016

No two consecutive integers sum to $100$.

$49$ and $51$ are the two consecutive odd integers whose sum is $100$.

#### Explanation:

Assuming the problem is asking what two consecutive integers sum to $100$, then there is no answer, as for any integer $n$, we have

$n + \left(n + 1\right) = 2 n + 1$, which is odd, while $100$ is even. Thus $2 n + 1 \ne 100$ for any integer $n$.

If the problem is asking for two consecutive odd integers whose sum is $100$, we can find them as follows:

Let $n$ be the lesser of the two odd integers, then we have

$n + \left(n + 2\right) = 100$

$\implies 2 n + 2 = 100$

$\implies 2 n = 98$

$\implies n = 49$

Thus the two consecutive odd integers are $49$ and $49 + 2 = 51$. Checking, we find that $49 + 51 = 100$, as desired.