Question

Find the sum of the first 50 terms of the arithmetic sequence whose general term is given.

$a_n=-3n+5$

Short answer

The obtained sum -3575.

Step-by-step solution

Step 1. Given Information.

The given general formula is $a_n=-3n+5$.

Step 2. Find the first and 50th terms. 

Substitute 1 for n in the formula for the first term.

$\begin{array}{rcl}{a}_1& =& -3\left(1\right)+5\\ & =& 2\end{array}$

Substitute 50 forn in the formula for the 50th term.

$\begin{array}{rcl}{a}_{50}& =& -3\left(50\right)+5\\ & =& -150+5\\ & =& -145\end{array}$

Step 3. Find the sum of 50th terms.

Use the formula of sum $S_n=\frac{n}{2}\left(a_1+a_n\right)$.

$\begin{array}{rcl}{S}_{50}& =& \frac{50}{2}\left(2-145\right)\\ & =& 25\left(-143\right)\\ & =& -3575\end{array}$