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 + Tn)
= 100/2 x (3 + 300)
= (100 x 303)/ 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.