Question

The sum of all odd integers between 2 and 100 divisible by 3 is ______.

Options

• 17

• 867

• 876

• 786

Answer 1

The sum of all odd integers between 2 and 100 divisible by 3 is 867.

Explanation:-

The numbers are 3, 9,15, 21, …, 99

Here a = 3, d = 6 and a_n = 99

∴ a_n = a + (n - 1 )d

⇒ 99 = 3 + (n - 1) x 6

⇒ 99 = 3 + 6n - 6

⇒ 6n = 102

⇒ n = 17

Required Sum `=n/2[a+a_n]=17/2[3+99]=17/2xx102=867`