Question

Find and algebraic expression to compute the sum of the first n terms of the arithmetic sequence with first term f and common difference d.

Answer 1

First term of an arithmetic sequence = f

Common difference = d

Therefore, the arithmetic sequence is f, f + d, f + 2d, f + 3d, …

This can also be written as f + (1 − 1)d, f + (2 − 1)d, f + (3 − 1)d, f + (4 − 1)d, …

Thus, its n^th term,

We know that the sum of a specified number of the consecutive terms of an arithmetic sequence is half the product of the number of the terms with the sum of the first and the last term.

∴ Sum of its first n terms = … (1)

Here,

Putting the values in equation (1):

Sum of first n terms =