Question

5 positive integers are in AP. the sum of three middle term is 24. product of first and 5th term is 48.find the terms of AP

Answer 1

☆☆ranshsangwan☆☆


Let those integers be a-2d, a-d, a, a+d & a+2d.
 By first condition, we get
3a=24.
a=8
By second condition,
(a-2d)(a+2d)=48
a^2-4d^2=48
4d^2=16
d=+2
For  both values of d, you get the same integers. But for positive value, they will be in ascending order while for negative value ,they will be in descending order.

Integers= 4, 6, 8, 10 & 12.

Answer 2

≡QUESTION≡

Five positive integer are in A.P the sum of middle 3 term is 24 and product of first and fifth term 48. Find the term of A.P.

                                                     

║⊕ANSWER⊕║

Series be a−2d, a−d, a, a+d, a+2d

The sum of first 3 terms

$a - d+a+a+d=24\\3a=24\\a = 8$

$(a+2d)(a-2d) = 48$

$a^{2} - 4d^{2} = 48$

Substitute a = 8

$64 - 4d^{2} = 48\\d^{2} = 16\\d = 2 \\ d = -2$

∴ The AP is 4,6,8,10,12