If a 1 + a 5 + a 10 + a 15 + a 20 + a 24 = 225 , then the sum of the first 24 terms of the arithmetic progression a 1 , a 2 , a 3 . . . . . is equal to

Question

If a 1 + a 5 + a 10 + a 15 + a 20 + a 24 = 225 , then the sum of the first 24 terms of the arithmetic progression a 1 , a 2 , a 3 . . . . . is equal to, 450, 675, 900, 1200

MARKS App · Accepted Answer

S = a 1 + a 2 + a 3 + . . . . + a 23 + a 24 S = 24 2 a 1 + a 24 = 12 a 1 + a 24 Given that, a 1 + a 5 + a 10 + a 15 + a 20 + a 24 = 225 ⇒ a 1 + a 1 + 4 d + a 1 + 9 d + a 24 - 9 d + a 24 - 4 d + a 24 = 225 ⇒ 3 a 1 + a 24 = 225 ⇒ a 1 + a 24 = 75 ⇒ S = 12 a 1 + a 24 = 12 × 75 = 900

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