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JEE Main20231 Feb 2023Morning ShiftMathematicsSequences and SeriesActual

Let a 1 = 8 , a 2 , a 3 , … . a n be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170 , then the product of its middle two terms is _____ .

Correct answer

0

Step-by-step solution

Let the common difference of an A.P. be d , then a 1 + a 2 + a 3 + a 4 = 50 ⇒ 4 a + 6 d = 50 ⇒ 32 + 6 d = 50 ⇒ d = 3 Also, a n - 3 + a n - 2 + a n - 1 + a n = 170 ⇒ 4 a + 4 n - 10 · d = 170 ⇒ 32 + 4 n - 10 · 3 = 170 ⇒ n = 14 So, middle terms are a 7 = a + 6 d = 26 ,   a 8 = a + 7 d = 29 ⇒ a 7 · a 8 = 754

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