Question

find sum of all two digit positive integers divisible by 3but not by 2

Answer 1

All two digit positive numbers which are divisible by 3 and not 2 are
15,21,27,33............99
First term=15
Common difference =6
Last term =99
Number of terms are 15
Sum =n/2(a+l)
Sum=15/2(15+99)
Sum=15/2(144)
Sum=1710/2
Sum of all numbers is 855

Answer 2

Answer: The sum of all  two digit positive integers is 855.

Step-by-step explanation:

Since we have given that

All two digit positive integers divisible by 3 but not by 2.

so, the sequence will be

$15,21,27,33,........99$

So, here, first term = 15

common difference = 21-15=6

last term = 99

so, number of terms will be

$a_n=a+(n-1)d\\\\99=15+(n-1)6\\\\99-15=6(n-1)\\\\84=6(n-1)\\\\\frac{84}{6}=n-1\\\\14=n-1\\\\n=15$

We need to find the sum of all two digit positive integers divisible by 3 but not by 2 is given by

$S_{15}=\frac{n}{2}(a+a_n)=\frac{15}{2}(15+99)=\frac{15}{2}\times 114=855$

Hence, the sum of all  two digit positive integers is 855.