Find the sum to $n$ terms of the $A.P.,$ whose $k^{\text {th }}$ term is $5 k+1$
Find the sum to $n$ terms of the $A.P.,$ whose $k^{\text {th }}$ term is $5 k+1$
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 $d=5$
$\Rightarrow a-d=1$
$\Rightarrow a-5=1$
$\Rightarrow a=6$
$S_{n}=\frac{n}{2}[2 a+(n-1) d]$
$=\frac{n}{2}[2(6)+(n-1)(5)]$
$=\frac{n}{2}[12+5 n-5]$
$=\frac{n}{2}[5 n+7]$
Similar Questions
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 $A.P.$
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 $A.P.$
Which of the following sequence is an arithmetic sequence
Which of the following sequence is an arithmetic sequence
Let $a_1=8, a_2, a_3, \ldots a_n$ be an $A.P.$ If the sum of its first four terms is $50$ and the sum of its last four terms is $170$ , then the product of its middle two terms is
Let $a_1=8, a_2, a_3, \ldots a_n$ be an $A.P.$ If the sum of its first four terms is $50$ and the sum of its last four terms is $170$ , then the product of its middle two terms is
- [JEE MAIN 2023]
Three numbers are in $A.P.$ whose sum is $33$ and product is $792$, then the smallest number from these numbers is
Three numbers are in $A.P.$ whose sum is $33$ and product is $792$, then the smallest number from these numbers is
The solution of the equation $(x + 1) + (x + 4) + (x + 7) + ......... + (x + 28) = 155$ is
The solution of the equation $(x + 1) + (x + 4) + (x + 7) + ......... + (x + 28) = 155$ is