### Home > PC3 > Chapter 12 > Lesson 12.1.2 > Problem12-27

12-27.

Calculate each of the following sums.

1. $10 + 10.5 + 11 + 11.5 + … + 90$

This is an arithmetic series with a common difference of $0.5$.

$S_n=\frac{n}{2}(a_1+a_2)$
$a_{1}$
and $a_{n}$ are given in the problem.
You need to determine $n$, which is the number of terms.

2. $20 + 20(1.05) + 20(1.05)^2 + 20(1.05)^3 + … + 20(1.05)^{20}$

3. $400−200+100−50+\dots+6.25$

Parts (b) and (c) are geometric series.
$S_n=\frac{a(1-r^n)}{1-r}$