Find the sum of the integers between 100 and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The sum of integers between $100$ and $200$ not divisible by $9$ is calculated as: (Sum of all integers between $100$ and $200$) $-$ (Sum of integ

Vedclass · Accepted Answer

$13167$

Vedclass · Answer

(B) The sum of integers between $100$ and $200$ not divisible by $9$ is calculated as: (Sum of all integers between $100$ and $200$) $-$ (Sum of integers between $100$ and $200$ divisible by $9$).Step $1$: Sum of all integers between $100$ and $200$ (i.e., $101, 102, \dots, 199$).Here, $a = 101$, $l = 199$, and $d = 1$.Number of terms $n = 199 - 101 + 1 = 99$.Sum $S_{99} = \frac{n}{2}(a + l) = \frac{99}{2}(101 + 199) = \frac{99}{2}(300) = 99 	imes 150 = 14850$.Step $2$: Sum of integers between $100$ and $200$ divisible by $9$.The first multiple of $9$ after $100$ is $108$ $(9 	imes 12)$ and the last is $198$ $(9 	imes 22)$.This forms an Arithmetic Progression: $108, 117, \dots, 198$.Here, $a = 108$, $l = 198$, $d = 9$.$198 = 108 + (n-1)9 \Rightarrow 90 = (n-1)9 \Rightarrow n-1 = 10 \Rightarrow n = 11$.Sum $S_{11} = \frac{11}{2}(108 + 198) = \frac{11}{2}(306) = 11 	imes 153 = 1683$.Step $3$: Required sum $= 14850 - 1683 = 13167$.

Find the sum of the integers between $100$ and $200$ that are not divisible by $9$.

Similar Questions

The $4^{\text{th}}$ term from the end of the $AP: -11, -8, -5, \dots, 49$ is

For the finite $A.P.$ $3, 5, 7, \ldots, 201$,find the $12^{th}$ term from the end.

For a given $A.P.$,the first term is $7$ and the $10^{th}$ term is $61$. Find the common difference of the $A.P.$ and its $25^{th}$ term.

The $n^{th}$ term of an $A.P.$ is given by $T_{n} = 5 - 6n$. Find the sum of the first $n$ terms of the $A.P.$

Which term of the $A.P.$ $13, 20, 27, 34, \ldots$ is $384$ (in $^{th}$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module