Question

the sum of the second and third term is 22 and the product of first and fourth term is AP of 50 find the first 4 terms

Answer 1

Let the four terms are a−3d, a−d, a+d, a+3d 
Now according to the question, a−d+ a+d= 222a = 22a = 11
Also, (a−3d)(a+3d )= 85 

a square− 9d square= 85 

121−9dsquare=85

 9 d square=121−85 = 36

d square = 4 d = ±2

So a = 11 and d = 2 or −2 

Now series is 11− 6, 11−2, 11+2, 11+6 or 5,9,13,17