QJEEM23Ma1170: JEE Main 2023 Mathematics - Class 11 JEEM23Ma1170 Solution: Let a 1 = 8 , a 2 , a 3 , … , a n be an A.P. If the sum of its…

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QJEEM23Ma1170: JEE Main 2023 Mathematics - Class 11 JEEM23Ma1170 Solution: Let a 1 = 8 , a 2 , a 3 , … , a n be an A.P. If the sum of its…

Let $a_{1} = 8, a_{2}, a_{3}, \dots, a_{n}$ 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 ___________.

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\begin{aligned} a_{1} + a_{2} + a_{3} + a_{4} = 50 \\ \Rightarrow 32 + 6 d = 50 \\ \Rightarrow d = 3 \\ and, a_{n - 3} + a_{n - 2} + a_{n - 1} + a_{n} = 170 \\ \Rightarrow 32 + (4 n - 10) \cdot 3 = 170 \\ \Rightarrow n = 14 \\ a_{7} = 26, a_{8} = 29 \\ \Rightarrow a_{7} \cdot a_{8} = 754 \end{aligned}

QJEEM23Ma1170: JEE Main 2023 Mathematics - Class 11 JEEM23Ma1170 Solution: Let a 1 = 8 , a 2 , a 3 , … , a n be an A.P. If the sum of its…

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