Question

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

$a_n=5n-1$

Short answer

The obtained sum is 6325.

Step-by-step solution

Step 1. Given Information.

The given general formula is $a_n=5n-1$.

Step 2. Find the first and 50th terms.

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

$\begin{array}{rcl}{a}_1& =& 5\left(1\right)-1\\ & =& 4\end{array}$

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

$\begin{array}{rcl}{a}_{50}& =& 5\left(50\right)-1\\ & =& 250-1\\ & =& 249\end{array}$

Step 3. Find the sum of 50th terms. 

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

$\begin{array}{rcl}{S}_{50}& =& \frac{50}{2}\left(4+249\right)\\ & =& 25\left(253\right)\\ & =& 6325\end{array}$