Question

what is common difference of four term in an ap such that the ratio of the product of first and fourth terms to that of second term and third is 2:3 and the sum of all four terms is 20​

Answer 1

answer : 2 or -2

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

Answer 2

Answer:

2

Step-by-step explanation:

this is the appropriate answer of your question