Answer
$\sum\limits_{i=1}^{5} 4n$
Work Step by Step
We want to find the explicit formula for the $nth$ term, so use the explicit formula for an arithmetic sequence, which is given by:
$a_{n} = a_{1} + (n - 1)d$, where $a_{n}$ is a certain term in a sequence, $a_{1}$ is the first term in the sequence, $n$ is the number of the term within the sequence, and $d$ is the common difference.
The common difference $d$ is found by subtracting one term in the sequence from the one directly following it:
$d = 8 - 4 = 4$
The common difference $d$ is $4$.
To find the explicit formula for the $nth$ term, plug in the values we know into the explicit formula for an arithmetic sequence:
$a_{n} = 4 + (n - 1)(4)$
Use distributive property:
$a_{n} = 4 + 4n - 4$
Combine like factors on the right side of the equation:
$a_{n} = 4n$
Now that we have the explicit formula to find the value of $n$, find the value of $n$ for the last term $20$ by plugging in $20$ into the explicit formula:
$20 = 4n$
Divide each side of the equation by $4$:
$n = 5$
This means that $20$ is the $5th$ and final term in this series.
Now, we can plug our values into the summation notation:
$\sum\limits_{i=1}^{5} 4n$