Question

find five number in a.p. whose sum is 12 and the ratio of the first to the last term is 2:3​

Answer 1

Sum of an AP is given by n/2(2a+(n-1)d)

since sum of first 5 term is given

so,

5/2(2a+4d)=25/2

a+2d=2/3.......(1)

and a/d=2/3......(2)

so, it value of a form (2) in (1)

2d/3+2d=5/2

so,

d=15/16 and a=2d/3=5/8

Therefore first five numbers are 5/8, 25/10, 40/10, 55/10, 70/10.