Question

Find the 4terms of the ap whose sum is 20 and product of the extreme is 16

Answer 1

Let the 4 terms of the AP be as follows :-

(a - 3d)

(a-d)

(a+d)

(a + 3d)

Now ,

The sum of the terms is 20

So,

a - 3d +a - d + a+ d + a +3d = 20

4a = 20

a= 20/4 = 5

Product of Extremes is 16

So,

(a - 3d)(a+3d) =16

a² - 9d² = 16

9d² =a² - 16

9d² = 25-16 = 9

d² = 1

d = 1

Now ,

a = 5

d= 1

So,

The AP is as follows :-

$a - 3d = 5 - 3 = 2 \\ \\ \\ a - d = 5 - 1 = 4 \\ \\ \\ a + d = 5 + 1 = 6 \\ \\ \\ a + 3d = 5 + 3 = 8$

So

The Arithmetic Progression is 2,4,6,8

Thanks!