Question

Find the sum of the first 50 terms of the arithmetic sequence whose general term is$a_n=2n-5$.

Short answer

The obtained sum is 2300.

Step-by-step solution

Step 1. Given Information.

The given general formula is$a_n=2n-5$.

Step 2. Find the first and 50th terms.

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

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

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

$\begin{array}{rcl}{a}_{50}& =& 2\left(50\right)-5\\ & =& 100-5\\ & =& 95\end{array}$

Step 3. Find the sum of 50th terms.

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

$\begin{array}{rcl}{S}_{50}& =& \frac{50}{2}\left(-3+95\right)\\ & =& 25\left(92\right)\\ & =& 2300\end{array}$