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8. Sequences and Series
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If $a_1, a_2, a_3, .... a_{21}$ are in $A.P.$ and $a_3 + a_5 + a_{11}+a_{17} + a_{19} = 10$ then the value of $\sum\limits_{r = 1}^{21} {{a_r}} $ is
A
$44$
B
$42$
C
$40$
D
$46$
Solution
Let $\,\,a_{3}+a_{19}=a_{5}+a_{17}=2 a_{11}=k$
given $\,\,a_{3}+a_{5}+a_{11}+a_{17}+a_{19}=10$
$\Rightarrow \frac{5}{2} \mathrm{k}=10 \Rightarrow \mathrm{k}=4$
$\text { so } a_{1}+a_{21}=4$ ….$(1)$
$\sum\limits_{r = 1}^{21} {{a_r} = \frac{{21}}{2}\left[ {{{\rm{a}}_1} + {{\rm{a}}_{21}}} \right] = 42} $
Standard 11
Mathematics
