Question

What is the common difference of four terms in an AP such that the ratio of the product of the first and fourth terms to that of the second and third is 2:3 and the sum of all four terms is 20 ?

(a) 3
(b) 1
(c) 4
(d) 2

I want a complete solution.

Most correct and fastest answer = Brainliest Answer ☺
​

Answer 1

Answer: (d)2

Step-by-step explanation:

Let four consecutive terms ; (a - 3d), (a - d) , (a + d), (a + 3d) are in AP.

a/c to question,

sum of all four terms is 20

or, (a - 3d) + (a - d) + (a + d) + (a + 3d) = 20

or, 4a = 20

or, a = 5......(1)

again a/c to question,

the ratio of the product of first and fourth terms to that of second term and third is 2:3.

so, (a - 3d)(a + 3d)/(a - d)(a + d) = 2/3

or, (a² - 9d²)/(a² - d²) = 2/3

or, 3a² - 27d² = 2a² - 2d²

or, a² = 25d²

from equation (1),

(5)² = 25d²

or, d² = 1 => d = ±1

here common difference = (a - d) - (a - 3d) = (a + d) - (a - d) = (a + 3d) - (a + d) = 2d

so, common difference = 2(±1) = ±2

Here is your answer mate ☝️

Answer 2

1000 hogye....!!

yayyyyyyy.....!!

Loveeee youuuuuuuu❤❤❤❤