Question

Find 4 no. In ap such that the sum of 2nd and 3rd terms is 22 and the product of 1st and 4 terms is 85

Answer 1

Answer:

The series of 4number is 5,9,13,17

Step-by-step explanation:

Let the four terms are a−3d, a−d, a+d, a+3d

Now, according to the question,

sum of 2nd and 3rd term is 22

a−d + a+d = 22

2a = 22

a = 11

Also,

(a−3d)(a+3d) = 85

$a^2-9d^2 = 85 \\121-9d^2=85 \\9d^2=121-85 = 36 \\d^2= 4$

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