Question

question
angela currently donates $1,500 per year to charity. each year she will donate an additional $75. how much money will angela have donated in total after 6 years?
select the correct answer below:
$8,250
$9,450
$9,675
$10,125

Explanation:

Step1: Identify the arithmetic - sequence elements

The first - term $a_1$ of the arithmetic sequence of annual donations is $a_1 = 1500$, and the common difference $d=75$, and $n = 6$.

Step2: Use the sum formula for an arithmetic sequence

The sum formula of the first $n$ terms of an arithmetic sequence is $S_n=\frac{n}{2}(2a_1+(n - 1)d)$.
Substitute $n = 6$, $a_1=1500$, and $d = 75$ into the formula:
\[

$$\begin{align*} S_6&=\frac{6}{2}(2\times1500+(6 - 1)\times75)\\ &=3(3000 + 5\times75)\\ &=3(3000+375)\\ &=3\times3375\\ & = 10125 \end{align*}$$

\]

Answer:

$10,125$