Question

find the sum of all numbers between 200 and 550 which are divisible by 9

Answer 1

The first number between 200&550 divisible by 9 is 207

& last number is 549.

So the numbers are,,,

207,216,225,...549

This form an AP with common difference d=9.

we have formula to find the numbers of integers . Let it is n

a(n) = a(1) +(n-1)d

549=207 +(n-1)9

342=9n-9

9n=351

n=39

So the sum of 39 integers

S(n)=n/2[a+l]

n=39

a=207

l=549

S(39)=39/2[207+549]

=39/2(756)

=39(378)

=14742