Question

The sum of four term in AP is 24 and their product is 945.Find the four term

Answer 1

Answer:

Let the terms be (a - 3d), (a - d), (a + d) and (a + 3d)

Given : Sum of the numbers in AP = 24

So, 

a - 3d + a - d + a + d + a + 3d = 24

4a = 24

a = 6

And the product of these four numbers is 945

So,

(a - 3d) (a - d) (a + d) (a + 3d) = 945

Putting the value of a =6

(6 - 3d) (6 - d) (6 + d) (6 + 3d) = 945

(36 - 9d²) (36 - d²) = 945

1296 - 360d² + 9d⁴ = 945

9d⁴ - 360d² + 1296 - 945 = 0

9d⁴ - 360d² + 351 = 0   Dividing it by 9 we get

d⁴ - 40d² + 39 = 0

d⁴ - 39d² - d² + 39 = 0

d²(d² - 39) - 1(d² - 39) = 0

(d² - 1) (d² - 39) = 0

d² - 1 = 0

d² = 1

d = √1

d = 1

d² - 39 = 0

d² = 39

d = √39

d = 6.244  

d = 6.244 is not possible, so d = 1

So, a = 6 and d = 1

The required four numbers of the AP are (6 - 3), (6 - 1), (6 + 1) and (6 + 3)

= 3, 5, 7 and 9

Answer.

hope it help u

by

Akshat Paliwal

Step-by-step explanation: