Question

Find the sum of the first 50 terms of the arithmetic sequence whose general term is$a_n=4n+3$.

Short answer

The obtained sum is 5250.

Step-by-step solution

Step 1. Given Information. 

The given general formula is $a_n=4n+3$.

Step 2. Find the first and 50th terms. 

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

$\begin{array}{rcl}{a}_1& =& 4\left(1\right)+3\\ & =& 7\end{array}$

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

$\begin{array}{rcl}{a}_{50}& =& 4\left(50\right)+3\\ & =& 200+3\\ & =& 203\end{array}$

Step 3. Find the sum of 50th terms. 

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

$\begin{array}{rcl}{S}_{50}& =& \frac{50}{2}\left(7+203\right)\\ & =& 25\left(210\right)\\ & =& 5250\end{array}$