# What four consecutive integers have a sum of 26?

May 8, 2016

color(blue)(5 + 6 +7+ 8 = 26")

#### Explanation:

Let the first number be $n$

Then the four consecutive numbers are:

$n \text{ ; "(n+1)" ; "(n+2)" ; } \left(n + 3\right)$

So :$\text{ } n + \left(n + 1\right) + \left(n + 2\right) + \left(n + 3\right) = 26$

$\implies 4 n + 6 = 26$

Subtract 6 from both sides

$\implies 4 n + 6 - 6 = 26 - 6$

$4 n + 0 = 26 - 6 \text{ }$

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Divide both sides by 4

$\frac{4}{4} \times n = \frac{20}{4}$

But $\frac{4}{4} = 1$

$n = 5$

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If the first number is 5 then the numbers are:

color(blue)(5 + 6 +7+ 8 = 26")