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
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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