Let $a_{1}=8, a_{2}, a_{3}, \ldots, a_{n}$ 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 ___________.
Answer (integer)
754
Solution
$$
\begin{aligned}
& a_1+a_2+a_3+a_4=50 \\\\
& \Rightarrow 32+6 d=50 \\\\
& \Rightarrow d=3 \\\\
& \text { and, } a_{n-3}+a_{n-2}+a_{n-1}+a_n=170 \\\\
& \Rightarrow 32+(4 n-10) \cdot 3=170 \\\\
& \Rightarrow \mathrm{n}=14 \\\\
& a_7=26, a_8=29 \\\\
& \Rightarrow a_7 \cdot a_8=754
\end{aligned}
$$
About this question
Subject: Mathematics · Chapter: Sequences and Series · Topic: Arithmetic Progression
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