Answer
This is an arithmetic sequence.
$a_5 = 125$
$a_6 = 150$
Work Step by Step
To find out if this is an arithmetic sequence, see if there is a common difference between terms:
$50 - 25 = 25$
$75 - 50 = 25$
$100 - 75 = 25$
There is a common difference of $25$; therefore, this is an arithmetic sequence.
Find the next two terms, $a_5$ and $a_6$, by using the explicit formula for arithmetic sequences, $a_n = a_1 + (n - 1)d$, where $d$ is the common difference. Use $a_1 = 45$ and $d = 25$.
Set up the equation to find $a_5$:
$a_5 = 25 + (5 - 1)25$
Simplify what is in parentheses first:
$a_5 = 25 + (4)25$
Multiply next:
$a_5 = 25 + 100$
Add to solve:
$a_5 = 125$
Set up the equation to find $a_6$:
$a_6 = 25 + (6 - 1)25$
Simplify what is in parentheses first:
$a_6 = 25 + (5)25$
Multiply next:
$a_6 = 25 + 125$
Add to solve:
$a_6 = 150$
