Question

In the following exercises, write the first five terms of the sequence whose general term is given$a_n=2n-7$

Short answer

The first five terms of the sequence whose general term is$a_n=2n-7$are$-5,-3,-1,1,3.$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thegeneraltermforthesequenceisgivenas}\\ a_n=2n-7\\ \text{Wehavetofindthefirstfivetermsofthesequence.}\end{array}$

Step 2. Calculating the first five terms.

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

$\begin{array}{cccccc}n& 1& 2& 3& 4& 5\\ a_n& \begin{array}{l}{a}_1=2\left(1\right)-7\\ =2-7\\ =-5\end{array}& \begin{array}{l}{a}_2=2\left(2\right)-7\\ =4-7\\ =-3\end{array}& \begin{array}{l}{a}_3=2\left(3\right)-7\\ =6-7\\ =-1\end{array}& \begin{array}{l}{a}_4=2\left(4\right)-7\\ =8-7\\ =1\end{array}& \begin{array}{l}{a}_5=2\left(5\right)-7\\ =10-7\\ =3\end{array}\end{array}$

Step 3. Conclusion

From the above step, we can conclude that the first five terms of the sequence will be $-5,-3,-1,1,3.$