Question

find the sum of all odd positive integets between 2 and 100 divisible by 3​

Answer 1

Step-by-step explanation:

the first odd positive integer between 2 and 100 by 3

9, 15, 21,27-------99

here

a=9

d=15-9=6

Tn=99

so,

tn=a+(n-1)d

$99 =9 + (n - 1)6 \\ 99 - 9 = (n - 1)6 \\ 90 = (n - 1)6 \\ 15 = n - 1 \\ n = 15 + 1 = 16$

now sum of term of 16th

$= ( \frac{16}{2} )(2 \times 9 + (16 - 1)9 \\ = \frac{16}{2} \times (18 + 135) \\ = 8 \times 153 \\ = 1224$

hence:-

the sum of all odd integers between 2 and 100 which divisible by 3 is 1224