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

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Answer 1 · 2016-01-20T11:54:04

#n->{9,11,13,15}#

#color(blue)("Building the equations")#

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

Then
term 1#->n#
term 2#->n+2#
term 3#->n+4#
term 4#->n+6#

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

Given that

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

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

Collecting like terms

#5n-4n=12-3#

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

term 1#->n->9#
term 2#->n+2->11#
term 3#->n+4->13#
term 4#->n+6->15#

#n->{9,11,13,15}#