Find the sum of all numbers between $200$ and $400$ which are divisible by $7.$
Find the sum of all numbers between $200$ and $400$ which are divisible by $7.$
The numbers lying between $200$ and $400 ,$ which are divisible by $7,$ are $203,210,217 \ldots .399$
$\therefore$ First term, $a=203$
Last term, $I=399$
Common difference, $d=7$
Let the number of terms of the $A.P.$ be $n.$
$\therefore a_{n}=399=a+(n-1) d$
$\Rightarrow 399=203+(n-1) 7$
$\Rightarrow 7(n-1)=196$
$\Rightarrow n-1=28$
$\Rightarrow n=29$
$\therefore S_{29}=\frac{29}{2}(203+399)$
$=\frac{29}{2}(602)$
$=(29)(301)$
$=8729$
Thus, the required sum is $8729 .$
Similar Questions
Let $\mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm{a}_{3}, \ldots$ be an $A.P.$ If $\frac{a_{1}+a_{2}+\ldots+a_{10}}{a_{1}+a_{2}+\ldots+a_{p}}=\frac{100}{p^{2}}, p \neq 10$, then $\frac{a_{11}}{a_{10}}$ is equal to :
Let $\mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm{a}_{3}, \ldots$ be an $A.P.$ If $\frac{a_{1}+a_{2}+\ldots+a_{10}}{a_{1}+a_{2}+\ldots+a_{p}}=\frac{100}{p^{2}}, p \neq 10$, then $\frac{a_{11}}{a_{10}}$ is equal to :
- [JEE MAIN 2021]
The $A.M.$ of a $50$ set of numbers is $38$. If two numbers of the set, namely $55$ and $45$ are discarded, the $A.M.$ of the remaining set of numbers is
The $A.M.$ of a $50$ set of numbers is $38$. If two numbers of the set, namely $55$ and $45$ are discarded, the $A.M.$ of the remaining set of numbers is
If the ${p^{th}}$ term of an $A.P.$ be $q$ and ${q^{th}}$ term be $p$, then its ${r^{th}}$ term will be
If the ${p^{th}}$ term of an $A.P.$ be $q$ and ${q^{th}}$ term be $p$, then its ${r^{th}}$ term will be
If the sum of the first $n$ terms of a series be $5{n^2} + 2n$, then its second term is
If the sum of the first $n$ terms of a series be $5{n^2} + 2n$, then its second term is
The sum of the first four terms of an $A.P.$ is $56 .$ The sum of the last four terms is $112.$ If its first term is $11,$ then find the number of terms.
The sum of the first four terms of an $A.P.$ is $56 .$ The sum of the last four terms is $112.$ If its first term is $11,$ then find the number of terms.