Question

12. Find the sum of the integers between 100 and 200
that are (1) divisible by 9 (11) not divisible 9​

Answer 1

Answer:

Sum = 13167

Step-by-step explanation:

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: a_n=a+(n-1)da

n

=a+(n−1)d

198=108+(n-1)9

n=11

Now we find sum of these 11 terms

Formula: S_n=\frac{n}{2}(2a+(n-1)d)S

n

=

2

n

(2a+(n−1)d)

S_{11}=\frac{11}{2}(108(2)+10(9))S

11

=

2

11

(108(2)+10(9))

Sum of 11 term = 1683

Now we find the sum of series 101,102,103,.........,199

S_{99}=\frac{99}{2}(101(2)+98(1))S

99

=

2

99

(101(2)+98(1))

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

THIS WAS FOR 2 ND PART AND FIRST IS SAME AS THIS JUST SLIGHT CHANGE LES IN VALUE

Answer 2

Step-by-step explanation:

divisble by 9

108+117....

sum= n/2(2a+(n-1)d)

sum= 11/2(2×108+(11-1)9)

sum= 11/2(216+90)

sum = 11/2×306

sum= 1683

not divisble by 9

101+102+......199

sum= sum of total - sum of divisble by 9

sum = 99/2(101+199)-1683

sum=150×99-1683

sum= 14850-1683=13167