Arithmetic Progression- Sum of N terms of an AP- Complete explanation with exam questions- CBSE C-10

Arithmetic Progression-Sum of N terms of an AP- Complete explanation with exam questions- CBSE Class 10
The sum of n terms of an AP is considered to be the sum of n consecutive terms of any arithmetic sequence. We can understand this by the example discussed below. Suppose we have to find the sum of all the terms from 1 to 100. The first way is to find the sum by adding all the terms individually but this process is very lengthy. Another method is to consider the sequence of 1, 2, 3,…, 98, 99, 100 as the group of 50 pairs taking then one from the beginning and from the end as,
1, 100), (2, 99), (3, 98),…

Sum of each pair is 101 and we have a total of 50 pairs, thus, the total sum will be

1+2+3+4+5+…+99+100 = 101×50 = 5050
Sn = n/2 [2a + (n-1)d]

where
n represents the number of terms of AP
a is the first term of the AP
d is the common difference of AP
Sum of n Terms = n/2(First Term + Last Term)




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