# What is the Sum of First 100 Positive Integers which are Divisible by 3?

getcalc.com's Arithmetic Progression (AP) calculator, formula & workout to find what's the sum of first 100 positive integers which are divisible by 3.

15150 is a sum of number series by applying the values of input parameters in the formula.

## Step by Step Calculation

The below workout with step by step calculation shows how to find the sum of first 100 positive integers which are divisible by 3, by applying arithmetic progression. It's one of the easiest methods to quickly find the sum of given number series.

step 1 Address the formula, input parameters & values.

Input parameters & values:

The number series 3, 6, 9, 12, 15, 18, 21, . . . . , 300.

The first term a = 3

The common difference d = 3

Total number of terms n = 100

step 2 apply the input parameter values in the AP formula

Sum = n/2 x (a + T_{n})

= 100/2 x (3 + 300)

= (100 x 303)/ 2

= 30300/2

3 + 6 + 9 + 12 + 15 + 18 + 21 + . . . . + 300 = 15150

Therefore, **15150** is the sum of first 100 positive integers which are divisible by 3.

## Definition & Formula

**Arithmetic Progression** often abbreviated as AP in mathematics, is one of a basic math functions represents the series of numbers or n numbers that having a common difference between consecutive terms. It's one of an easiest methods to find the total sum of any number series that follows arithmetic progression. It's very useful function in mathematics to find the sum of series that having large set of numbers that follows arithmetic progression.