Sum to n terms of A.P., whose k^{text {th }} term is 5 k+1

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8. Sequences and Series

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Find the sum to $n$ terms of the $A.P.,$ whose $k^{\text {th }}$ term is $5 k+1$

A

$\frac{n}{2}[5 n+7]$

B

$\frac{n}{2}[5 n+7]$

C

$\frac{n}{2}[5 n+7]$

D

$\frac{n}{2}[5 n+7]$

Solution

It is given that the $k^{\text {th }}$ term of the $A.P.$ is $5 k+1$

$k^{\text {th }}$ term $=a_{k}+(k-1) d$

$\therefore a+(k-1) d=5 k+1$

$a+k d-d=5 k+1$

$\therefore$ Comparing the coefficient of $k ,$ we obtain $d=5$

$\Rightarrow a-d=1$

$\Rightarrow a-5=1$

$\Rightarrow a=6$

$S_{n}=\frac{n}{2}[2 a+(n-1) d]$

$=\frac{n}{2}[2(6)+(n-1)(5)]$

$=\frac{n}{2}[12+5 n-5]$

$=\frac{n}{2}[5 n+7]$

Standard 11

Mathematics

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