Question

Divide 48 into four parts which are in AP such that the product of extremes to the product of means is 7:15.

Answer 1

Answer:

3,9,15,21

Step-by-step explanation:

Let the four parts be a - 3d, a - d, a + d, a + 3d.

(a - 3d) + (a - d) + (a + d) + (a + 3d) = 48

a - 3d + a - d + a + d + a + 3d = 48

4a = 48

a = 12.

Now,

[(a - 3d)(a + 3d)]/[(a - d)(a + d)] = 7/15

[(12 - 3d)(12 + 3d)/[(12 - d)(12 + d)] = 7/15

[144 - 9d²]/[144 - d²] = 7/15

15(144 - 9d²) = 7(144 - d²)

2160 - 135d² = 1008 - 7d²

2160 - 1008 = -7d² + 135d²

1152 = 128d²

1152/128 = d²

9 = d²

d = ±3.

When d = 3:

a - 3d = 12 - 3(3) = 3

a - d = 12 - 3 = 9

a + d = 15

a + 3d = 12 + 3(3) = 21.

When d = -3:

a - 3d = 12 - 3(-3) = 21

a - d = 12 - (-3) = 15

a + d = 12 + (-3) = 9

a + 3d = 12 + 3(-3) = 3

Hence, the AP is 3,9,15,21.

Hope it helps you

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