Question

Find the sum of all two digit positive integers which are divisible by 3 but not by 2

Answer 1

let a=12
d=15-12=3
an=99
an=a+n-1×d
99=12+n-1×3
99=12+3n-3
99=9+3n
3n=99-9
3n=90
n=90/3
n=30

Answer 2

Answer:

Step-by-step explanation:

The two digit positive integers starts from 11 nd end at 99

So the no. Divisible by 3 are - 12,15,18.........99

Bt here they have said that the no. Must be divisible by 3 but not by 2..

So we hv to cancel out the no that are divisible by 2

After that we get the series as- 15,21,27,33.....99

To find their sum we require the total no.of terms

Therefore using the formula

a+(n-1)d

Here a=15, d=21-15=6, l=99

Substituting the values we get

15+(n-1)6=99

15+6n-6=99

9+6n=99

6n=90

n=15

Now to find their sum we use the formula n/2{a+l}

15/2(15+99)

7.5(15+99)

7.5(114)

=855 which is the final answer...