Question

The sum of five numbers in ap is 40. The product of the first and last is 28. Find the numbers.

Answer 1

here
are the five numbers are
a-2d,a-d,a,a+d,a+2d

from 1st condition
a-2d+a-d+a+a+d+a+2d=40
5a=40
a=40/5
a=8

from 2nd condition
(a-2d)(a+2d)=28
(8-2d)(8+2d)=28
64+16d-16d-4d=28
64-4d=28
-4d=28-64
-4d=-36
d=-36/-4
d=9

therefore the numbers is
a-2d=8-2×9=8-18=-10
a-d=8-9=-1
a=8
a+d=8+9=17
a+2d=8+2×9=8+18=26

therefore five numbers is -10,-1,8,17,26