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Find the sum of all odd integers between 2 and 100 divisible by 3.

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452

754

867

765

answer is C.

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Detailed Solution

We need to find the sum of all odd integers between 2 and 100 which is divisible by 3.
The numbers are 3, 9, 15, …...99.
Common difference, d=9-3

\Rightarrow

d=6
The

n^{th}

term of AP is

a_{n} = a + (n - 1) d

a = 3

d

= 6

a_{n} = 99

\Rightarrow 99 = 3 + (n - 1) 6

\Rightarrow 96 = 6 (n - 1)

\Rightarrow n - 1 = 16

\Rightarrow n = 17

Sum of n terms in AP is

S_{n} = \frac{n}{2} (a + l)

Here

{l = a}_{n} = 99

S_{17} = \frac{17}{2} (3 + 99)

S_{17} = 867

Hence, the required sum is 867.
Therefore, option 3 is correct

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