Sum of the first N terms of the series 5,12, 23, 38….
Given a number N, the task is to find the sum of first N terms of the below series:
Sn = 5 + 12 + 23 + 38 + … upto n terms
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Input: N = 2 Output: 17 5 + 12 = 17 Input: N = 4 Output: 80 5 + 12 + 23 + 38 = 78
Approach: Let, the nth term be denoted by tn.
This problem can easily with the help of a general formula for these type of series,
The series given above is a quadratic series. They are special because the difference of consecutive terms of this series will be in arithmetic progression.
There general formula is given by:
General Formula = a*(n^2) + b*n + c
Now, by putting first 3 terms of series in general formula we can get values of a, b and c.
Sn = 5 + 12 + 30 + 68 + ...... tn = 2 * (n^2) + n + 2 Sn = 2 * (n * (n+1) * (2 * n+1)/6) + n * (n+1)/2 + 2 * (n)
Below is the implementation of above approach:
Sum = 40