When 9^{th} term of A.P is divided by its 2^{nd} term then quotient is 5 and when 13^{th} term is di

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8. Sequences and Series

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When $9^{th}$ term of $A.P$ is divided by its $2^{nd}$ term then quotient is $5$ and when $13^{th}$ term is divided by $6^{th}$ term then quotient is $2$ and Remainder is $5$ then find first term of $A.P.$

A

$2$

B

$3$

C

$4$

D

$5$

Solution

given $\Rightarrow \mathrm{T}_{9}=5 \mathrm{T}_{2} $ and $ \mathrm{T}_{13}=2 \mathrm{T}_{6}+5$

so $a+8 d=5(a+d) $ and $a+12 d=2(a+5 d)+5$

$\Rightarrow a=3$

Standard 11

Mathematics

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