Question

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

Answer 1

$15 + 21 + 27......... + 99$

Hence,

$a = 15 \\ d = 6 \\ a_{n} = 99$

We Know That:-

$s_{n} = \frac{n}{2} \times (a + a_{n})$

Hence,

$a_{n} = a + (n - 1)d \\ 99 = 15 + (n - 1)6 \\ 84 = 6n - 6 \\ 90 = 6n \\ n = 15$

Now,

$s_{n} = \frac{15}{2} \times 114 \\ = 15 \times 57 \\ = 855$

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