If sum of n terms of an A.P. is 3{n^2} + 5n and {Tₘ} = 164 then m =

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8. Sequences and Series

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If sum of $n$ terms of an $A.P.$ is $3{n^2} + 5n$ and ${T_m} = 164$ then $m = $

A

$26$

B

$27$

C

$28$

D

None of these

Solution

(b) Obviously,

$164 = (3{m^2} + 5m) – \{ 3{(m – 1)^2} + 5(m – 1)\} $

$ = (3{m^2} + 5m) – 3{m^2} + 6m – 3 – 5m + 5$

$ \Rightarrow $$164 = 6m + 2$

$ \Rightarrow $$m = 27$.

Standard 11

Mathematics

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