# How do you find all sets of three consecutive even integers whose sum is between 25 and 45?

Mar 12, 2016

solutions are: 8 10 12
or 10,12,14
or 12,14,16

#### Explanation:

Let the first even number be n. The sum will be n+n+2+n+4=3 n + 6 and

25 < 3 n + 6 < 45.
19<3n<39
So, $\frac{19}{3} < n < \frac{39}{3}$.
$\implies 6 \frac{1}{3} < n < 13$ As n is an even integer,
$8 \le n \le 12$
possible values of n = 8,10,12

For the starter n = 8, the sum is 8 + 10 +12 = 30.

for n= 10 there exists thee numbers 10.12,14,where sum =36
for n= 12 there exists thee numbers 12,14,16,where sum =42

Hence sets of three consecutive numbers are
set1 $\implies 8 , 10 , 12$
or
set2$\implies 10 , 12 , 14$
or
set3 $\implies 12 , 14 , 16$