Question

this was the question of business mathematics ch AP

Answer 1

We have to find the number of integers and their sum.

The first integer that is divisible by 3 between 10 & 100 is 12.

& The last integer is 99.

The integers are divisible by 3, so all the integers are +3 of the integer before them.

12,15,18...99

This forms an Ap with common difference d=3.

Let the number of integers is n.

So the nth integer will be the last one ie. 99

The formula

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

99=12+(n-1)3

87=3n-3

3n=90

n=30

So there are 30 integers between 10 &100 divided by 3.

And their sum..

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

n=30

a=12

l=99

s(30) = (30/2)[12+99]

s(30)=15x111

=1665