Question

In the following exercises, write the first five terms of the sequence whose general term is given.

$a_n=5n-1$

Short answer

The first five terms of the sequence whose general term is$a_n=5n-1$are$4,9,14,19,24$.

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thegeneraltermforthesequenceisgivenas}\\ a_n=5n-1\\ \text{Wehavetofindthefirstfivetermsofthesequence.}\end{array}$

Step 2. Calculating the first five terms.

$\begin{array}{l}\text{Wewillsubstitute}n=1,2,3,4\text{and}5\text{intheordertoobtainthefirstfivetermsofthesequence.}\\ \text{Now,}\end{array}$

$\begin{array}{cccccc}n& 1& 2& 3& 4& 5\\ a_n& \begin{array}{l}{a}_1=5\left(1\right)-1\\ =5-1\\ =4\end{array}& \begin{array}{l}{a}_2=5\left(2\right)-1\\ =10-1\\ =9\end{array}& \begin{array}{l}{a}_3=5\left(3\right)-1\\ =15-1\\ =14\end{array}& \begin{array}{l}{a}_4=5\left(4\right)-1\\ =20-1\\ =19\end{array}& \begin{array}{l}{a}_5=5\left(5\right)-1\\ =25-1\\ =24\end{array}\end{array}$

Step 3. Conclusion

From the above step, we can observe that the first five terms of the sequence will be$4,9,14,19,24$