# The sum of 6 consecutive integers is 393. What is the third number In this sequence?

Dec 10, 2016

65

#### Explanation:

Let's define the first integer as $x$. Then the next five consecutive integers would be:

$x + 1$, $x + 2$, $x + 3$, $x + 4$ and $x + 5$.

The sum of these six integers is 393 so we can write:

$x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 = 393$

$6 x + 1 + 2 + 3 + 4 + 5 = 393$

$6 x + 15 = 393$

$6 x + 15 - 15 = 393 - 15$

$6 x + 0 = 378$

$\frac{6 x}{6} = \frac{378}{6}$

$x = 63$

Because the first integer is 63 then the third would be $x + 2$ or $63 + 2 = 65$