Question

Find the sum of all odd numbers lying between 101 and 200 which are divisible by 3.

Answer 1

Odd numbers between 101 and 200 that are divisible by 3 form an AP: 105, 111, 117, …, 195

a = 105

d = 6

l = 195

Using the n^th term formula:

l  = a + (n − 1)d

195 = 105 + (n − 1)6

195 - 105 = (n − 1)6

90 = (n − 1)6

`90/6 = (n − 1)`

15 = n − 1

15 + 1 = n

n = 16

`S_n = n/2 (a + l)`

`S_16 = 16/2 (105 + 195)`

= 8 × 300

= 2,400