An arithmetic sequence or progression is defined as a sequence of numbers in which for every pair of consecutive terms, the second number is obtained by adding a fixed number to the first one.
Sum of N Terms of A.P.
For any progression, the sum of n terms can be easily calculated. For an AP, the sum of the first n terms can be calculated if the first term and the total terms are known. The formula for the arithmetic progression sum is explained below:
Consider an AP consisting of “n” terms.
| S = n/2[2a + (n − 1) × d] |
Formula to find the sum of AP when first and last terms are given as follows:
| S = n/2 (first term + last term) |
Solution
For AP,
an = a+ (n-1)d = 2n-1
a1 = 2-1 = 1
a2 = 4-1 = 3
Common difference , d = 3-1 = 2
Sum of n terms = (n/2)(2a + (n-1)d)
= (n/2)(2+(n-1)2)
= (n/2)(2+2n-2)
= (n/2)2n
= n2
Check out the video given below to know more about sequence and series
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