Question

☺Heya,☺

Please solve this question:-

Q. Find the sum of integers between 100 and 200:

(1) Divisible by 9

(2) Not divisible by 9​

Answer 1

The sum integers between 100 and 200 that are not divisible by 9.
First we find how many numbers between 100 and 200 divisible by 9
First term (a) = 108
Common Difference (d) = 9
Last term (l)=198
Formula:
198=108+(n-1)9
n=11
Now we find sum of these 11 terms
Formula:

Sum of 11 term = 1683
Now we find the sum of series 101,102,103,.........,199

Sum of 99 terms = 14850
Sum of integers between 100 and 200 not divisible by 9 = 14850 - 1683 = 13167
Hence, The sum of number not divisible by 9 between 100 and 200 is 13167

Answer 2

hello here is your answer............................

100/9 which gives 1 as remainder

so 99+9 = 108

first number is 108 divisible by 9 which gives no remainder

200/9 which gives 2 as remainder

so 200-2 = 198

last number is 198 divisible by 9 gives no remainder

sum of numbers which are divisible by 9 between 100 and 200 =((no of terms) ((first number * 2) + ( 9 * ((no of terms) - 1)))/2

sum of no divisible by 9 = 11((2*108)+(9*(11-1))/2

sum of no divisible by 9 = 5.5(216+90) = 306*5.5 = 1683

sum of numbers between 100 and 200 = 99(2*101+98*1)/2 = 99(202+98)/2 = 99(300)/2 = 99(150) = 14850

sum of number between 100 and 200 which are not divisible by 9 = (sum of numbers between 100 and 200) - (sum of number which are divisible by 9 between 100 and 200) = 14850-1683 = 13167