Question

find five consecutive terms in an A.P. whose sum is 50 and product of first and fourth term is 28

Answer 1

Let the first 5 terms be a, a+d, a +2d, a+3d, a+4d.

a+(a+3d)=28. (given)
2a+3d=28
a=14-(3d/2)---------(1)

a+a+d+a+2d+a+3d+a+4d=50. (given)
5a+10d=50
a+2d=10.

From (1)
14 - 3d/2 +2d= 10
d/2= -4
d=-8

Put value of d in (1)

a=14+ (24/2)
a=26.

five consecutive terms in an A.P are 26, 18, 10, 2, -6.