# Arithmetic progression

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• Jan 12th 2010, 03:33 AM
mastermin346
Arithmetic progression
Find the number of terms between 100 and 200 that are divisible by 3.
• Jan 12th 2010, 03:37 AM
mathaddict
Quote:

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 $T_n=a+(n-1)d$

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

Solve for n .
• Jan 12th 2010, 04:43 AM
HallsofIvy
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.