# The sum of four consecutive odd integers is three more than 5 times the least of the integers, what are the integers?

Jan 20, 2016

$n \to \left\{9 , 11 , 13 , 15\right\}$

#### Explanation:

$\textcolor{b l u e}{\text{Building the equations}}$

Let the first odd term be n
Let the sum of all the terms be s

Then
term 1$\to n$
term 2$\to n + 2$
term 3$\to n + 4$
term 4$\to n + 6$

Then
$s = 4 n + 12$ .................................(1)

Given that

$s = 3 + 5 n$..................................(2)
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Equating (1) to (2) thus removing the variable s

$4 n + 12 = s = 3 + 5 n$

Collecting like terms

$5 n - 4 n = 12 - 3$

$n = 9$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Thus the terms are:

term 1$\to n \to 9$
term 2$\to n + 2 \to 11$
term 3$\to n + 4 \to 13$
term 4$\to n + 6 \to 15$

$n \to \left\{9 , 11 , 13 , 15\right\}$