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

(C) 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

(C) 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 $200$.The integers are $101, 102, \dots, 199$. This is an Arithmetic Progression $(AP)$ with $a = 101$, $l = 199$, and $d = 1$.Number of terms $n$: $199 = 101 + (n - 1)1 \implies n - 1 = 98 \implies n = 99$.Sum $S_{99} = \frac{99}{2}(101 + 199) = \frac{99}{2}(300) = 99 	imes 150 = 14850$.Step $2$: Sum of integers between $100$ and $200$ divisible by $9$.The first integer divisible by $9$ after $100$ is $108$ $(9 	imes 12)$ and the last is $198$ $(9 	imes 22)$.This is an $AP$ with $a = 108$, $l = 198$, $d = 9$.Number of terms $n$: $198 = 108 + (n - 1)9 \implies 90 = (n - 1)9 \implies n - 1 = 10 \implies n = 11$.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 $10^{\text{th}}$ term of the $AP: 5, 8, 11, 14, \ldots$ is

The sum of the first $30$ positive multiples of $6$ is:

For an $A.P.$,the first term is $10$,the $n^{th}$ term is $40$,and the sum of the first $n$ terms is $150$. Find the value of $n$ and the common difference $d$.

$A$ person saved $Rs. 16,500$ in all during $10$ years. After the first year,every year he saved $Rs. 100$ more than what he had saved the previous year. Find his savings of the first year.

Write the first three terms of the $APs$ when $a$ and $d$ are as given below:
$a = \sqrt{2}, d = \frac{1}{\sqrt{2}}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module