Question

Four terms are in A.P. if the sum of two extreme terms is 8
& and the product of mean terms 15. Two tèrms will be:
"(a)3,7 (6)3,9 (c) 1,4 (d) 2,4​

Answer 1

Given :-

Four terms are in A.P

Sum of extreme is 8 and product of

mean is 15.

To find :-

The two terms.

Solution:-

Let the four terms in AP be a + 2d , a + d , a - d , a - 2d.

A/Q.

→$a + 2d + a - 2d = 8$

→$2a = 8$

→$a = \dfrac{8}{2}$

→$a = 4$

Now,

→$( a+d) (a-d) = 15$

→$a^2 - d^2 = 15$

→$(4)^2 - d^2 = 15$

→$16 -d^2 = 15$

→$-d^2 = 15 -16$

→$-d^2 = -1$

→$d = \sqrt{1}$

→$d = \pm 1$

Hence,

The terms is A.P will be :-

a + d = 4 + 1 = 5

a - d = 4 - 1 = 3

a + 2d = 4 + 2 × 1 = 4 + 2 = 6

a - 2d = 4 - 2 × 1 = 4 - 2 = 2