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8. Sequences and Series
medium
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
