The sum and product of three respective terms in AP is 15 and 80 . find the terms of an arthmetic progressions.
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Let the first term be a and common difference be d.
The three terms are,
a−d,a,a+d
As, the sum of three terms is 15, then,
a−d+a+a+d=15
3a=15
a=5
As, the product of three terms is 80, then,
(5−d)5(5+d)=80
5(25−d
2
)=80
25−d
2
=16
d
2
=9
d=±3
The numbers are 2,5,8 or 8,5,2.
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