Thread: Arithmetic progression

Find the number of terms between 100 and 200 that are divisible by 3.

Originally Posted by mastermin346

Find the number of terms between 100 and 200 that are divisible by 3.

HI

The set of numbers within the given range which are divisible by 3 would be

102 , 105 , 108 , ... , 198

Using $\displaystyle T_n=a+(n-1)d$

$\displaystyle
198=102+(n-1)(3)
$

Solve for n .

perhaps simpler: there are 99 numbers between 100 and 200. Since every third number is divisible by 3, there are 99/3= 33 numbers between 100 and 200 that are divisible by 3.