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8. Sequences and Series
medium
यदि $a _{1}, a _{2}, a _{3}, \ldots \ldots \ldots, a _{ n }$ एक समान्तर श्रेढ़ी में है तथा $a_{1}+a_{4}+a_{7}+\ldots \ldots . .+a_{16}=114$, है, तो $a_{1}+a_{6}+a_{11}+a_{16}$ बराबर है
A
$76$
B
$64$
C
$98$
D
$38$
(JEE MAIN-2019)
Solution
${a_1} + {a_4} + {a_{ 7}} + {a_{10}} + {a_{13}} + {a_{16}} = 114$
$ \Rightarrow \frac{6}{2}\left( {{a_1} + {a_{16}}} \right) = 114$
${a_1} + {a_{16}} = 38$
So, ${a_1} + {a_6} + {a_{ 11}} + {a_{16}} = \frac{4}{2}\left( {{a_1} + {a_{16}}} \right)$
$ = 2 \times 38 \Rightarrow 76$
Standard 11
Mathematics
