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12 terms.

Sum_of_ap = n(2a + (n-1)d) ÷ 2

For 43, 39, 35, ... a = 43, d = -4

⇒ 252 = n(2 x 43 + (n - 1) x -4) ÷ 2

⇒ 252 = 45n -2n2

⇒ 2n2 - 45n + 252 = 0

⇒ (2n - 21)(n - 12) = 0

⇒ n = 101/2 or 12

101/2th terms do not make sense, so cannot be an answer. Thus 12 terms are needed.

What happens is that the sum increases whilst the terms are positive. After 10 terms, the sum is still less than 252. The 11th term is the last positive term and takes the sum over 252; the 12th term is the first negative term and takes the sum back down to 252.

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โˆ™ 2012-01-14 16:21:56
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Q: How many terms of the ap 43 39 35 ... be taken so that their sum is 252?
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