# Find the Sum: 1 + 2 + 3 + 4 + 5 + ….. + 100

By K Balaji|Updated : November 9th, 2022

The sum 1 + 2 + 3 + 4 + 5 + ….. + 100 is 5050.

Arithmetic Progression -

It is known as the AP sequence because it always has a consistent difference between two consecutive phrases.

When we study Arithmetic Progression, which is associated with: There are two key formulas we encounter:

The nth term of AP

Tn = a + (n-1) d

Sum of the first n terms

Sn = n/2 (a + 1)

### Types of Arithmetic Progression

Finite AP: Finite APs are defined as having a finite number of terms. A last term exists in a finite AP.

For example: 3,5,7,9,11,13,15,17,19,21

Infinite AP: An infinite AP is one that doesn't have a finite number of terms. Such APs lack a final term.

For example: 5,10,15,20,25,30, 35,40,45………………

Now we have to calculate the sum of the given series:

Given series: 1, 2, 3, 4, 5, ….., 100

From the above series it is confirmed that the given series is in arithmetic progression.

Therefore the first term of the progression, a = 1

The last term of the progression l = 100

The number of terms of the progression, n = 100

Thus, the sum of the given series can be given by

Sn = n/2 (a + 1)

S100 = 100/2 (1 + 100)

S100 = 50 x 101

On simplifying we get

S100 = 5050

Summary:-

## Find the Sum: 1 + 2 + 3 + 4 + 5 + ….. + 100

Therefore the sum 1 + 2 + 3 + 4 + 5 + ….. + 100 is 5050. Because there is always a difference between two consecutive sentences, it is known as the AP sequence.

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