The sum of the first n terms of an arithmetic progression (A.P.) is the sum of the values of the first n elements of the sequence. Formula: $$S_n = \sum_{i...
The sum of the first n terms of an arithmetic progression (A.P.) is the sum of the values of the first n elements of the sequence.
Formula:
Where:
(S_n) is the sum of the first n terms
(a_i) is the (i)-th term in the sequence
Example:
Consider the sequence (a_1 = 1, a_2 = 3, a_3 = 5). The sum of the first 3 terms would be:
Additional Notes:
If the first term is 0, the sum will be equal to the second term.
The sum of the first n terms can be calculated directly by adding the values of the first n terms of the sequence.
The sum of the first n terms of an A.P. can also be calculated using the formula (S_n = \frac{n}{2} a_1 + \left(n - 1\right)d) where (a_1) is the first term, (d) is the common difference between consecutive terms, and (n) is the number of terms in the sequence