Question

Find the sum of the first 63 terms of –19, -13, -7 …

Answer 1

You can tell this is an arithmetic sequence because it is a list of terms beginning with -19 that increase by 6 each term. Because of this, we can use the formula for the sum of an arithmetic sequence, which is:

$S = \dfrac{n}{2}[2 a_1 + d(n - 1)]$

• $n$ is the number of terms in the sequence
• $a_1$ is the starting term
• $d$ is the common difference among the terms

In this case, we can see that $n = 63$, $a_1 = -19$, and $d = 6$. Thus, we can use the formula:

$S = \dfrac{63}{2} [2(-19) + 6(62)] = 10,521$

Our answer is 10,521.