The sum of four numbers in an arithmetic progression is 48 and the ratio of the product of the extremes to the product of the two middle terms is 27 : 35 , then the largest term of this arithmetic progression is

Question

The sum of four numbers in an arithmetic progression is 48 and the ratio of the product of the extremes to the product of the two middle terms is 27 : 35 , then the largest term of this arithmetic progression is, 10, 12, 14, 18

MARKS App · Accepted Answer

Let the A. P. be a - 3 d , a - d , a + d , a + 3 d The sum of the terms = 48 = 4 a ⇒ a = 12 Given, 12 - 3 d 12 + 3 d 12 - d 12 + d = 27 35 ⇒ 9 4 - d 4 + d 12 - d 12 + d = 27 35 ⇒ 16 - d 2 35 = 144 - d 2 3 ⇒ 35 d 2 - 3 d 2 = 16 × 35 - 144 × 3 ⇒ 32 d 2 = 16 35 - 27 = 16 × 8 ⇒ d 2 = 4 ⇒ d = ± 2 So the numbers are: 6,10,14,18

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