Question

37. The sum of first three terms in an arithmetic progression is 24 and the sum of their squares is 224. Find the first three terms of this arithmetic progression.

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Answer 1

12, 8, and 4

Explanation:

• Given

a + d + a + a - d = 24

3a = 24 ⇒ [ a = 8 ]

and (a + d)² + a² + (a - d)² = 224

3a² + 2d² = 224

2d² = 224 - 192 = 32

d² = 16

[ d = ±4 ]

∴ The first three terms to A.P are

a + d = 8 + 4 = 12

a - = 8

a - d = 8 - 4 = 4

∴ Three terms are 12 , 8, and 4