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8. Sequences and Series
medium
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
A
$753$
B
$752$
C
$754$
D
$751$
(JEE MAIN-2023)
Solution
$a_1+a_2+a_3+a_4=50$
$\Rightarrow 32+6 d=50$
$\Rightarrow d=3$
and, $a_{n-3}+a_{n-2}+a_{n-1}+a_n=170$
$\Rightarrow 32+(4 n -10) \cdot 3=170$
$\Rightarrow n =14$
$a _7=26, a _8=29$
$\Rightarrow a _7 \cdot a _8=754$
Standard 11
Mathematics
