Do not understand what is meant by "in terms of n" I took calculus 5 years ago so I am unaware of what is meant by in terms of the variables in this summation example.
specifically these two questions. please help me understand what the steps are to solving these.
I was unable to google my malfunction.

What is the value of the following summation in terms of $n$: $\sum\limits_{=+1}^{3} (2−3)$?

Determine the value of this summation, in terms of $a$, $b$, $c$ and $d$. Assume that $a &lt; b$ and that all four are positive integers. $\sum\limits_{=}^{b} (+)$.
When we say expression in terms of $n$, your final answer should be an expression involving $n$.
For your problem, I will help you with the first one but I will leave the second one to you.
\begin{align}\sum_{i=n+1}^{3n}(2i-3)&amp;=2\sum_{i=n+1}^{3n}i - 3\sum_{i=n+1}^{3n}1 \\
&amp;=2[(n+1) + (n+2) + \ldots + 3n]-3(2n)\\
&amp;= 2 \cdot \frac{2n}{2}\left[(n+1)+3n \right]-6n\end{align}
Try to simplify the expression above.  As you can see, the final answer involves $n$.
To compute the second sum, you can write
$\sum_{i=a}^b (ci + d) = c(\sum_{i=1}^b i - \sum_{i=1}^{a-1} i) + d (b-a+1)$
and apply the formula for the sum of consecutive integers $\sum_{k=1}^n k = n(n+1)/2$.