Explain how to find the sum of the first n terms of an arithmetic sequence.

To find the sum of the first n terms of an arithmetic sequence, use the formula Sn = n/2(2a + (n-1)d).

An arithmetic sequence is a sequence of numbers where each term is obtained by adding a fixed number (d) to the previous term. The first term is denoted by 'a'. To find the sum of the first n terms of an arithmetic sequence, we use the formula Sn = n/2(2a + (n-1)d).

Let's take an example to understand this formula better. Consider the arithmetic sequence 3, 7, 11, 15, 19, ... The first term (a) is 3 and the common difference (d) is 4. To find the sum of the first 5 terms (n=5), we substitute the values in the formula:

Sn = n/2(2a + (n-1)d)
= 5/2(2(3) + (5-1)4)
= 5/2(6 + 16)
= 5/2(22)
= 55

Therefore, the sum of the first 5 terms of the arithmetic sequence 3, 7, 11, 15, 19, ... is 55.

It is important to note that the formula for the sum of an arithmetic sequence only works if the sequence is finite. If the sequence is infinite, the sum cannot be found using this formula.