Question

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

$a_n={\left(-1\right)}^n\cdot 3n$

Short answer

The first five terms of the sequence whose general term is$a_n={\left(-1\right)}^n\cdot 3n$are$-3,6,-9,12,-15.$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thegeneraltermisgivenas}\\ a_n={\left(-1\right)}^n\cdot 3n\\ \text{Wehavetofindthefirstfivetermsofthesequence.}\end{array}$

Step 2. Step 2. Calculating the terms 

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

$\begin{array}{cccccc}n:& 1& 2& 3& 4& 5\\ a_n:& \begin{array}{l}{a}_1={\left(-1\right)}^1\cdot 3\left(1\right)\\ =-1\cdot 3\\ =-3\end{array}& \begin{array}{l}{a}_2={\left(-1\right)}^2\cdot 3\left(2\right)\\ =1\cdot 6\\ =6\end{array}& \begin{array}{l}{a}_3={\left(-1\right)}^3\cdot 3\left(3\right)\\ =-1\cdot 9\\ =-9\end{array}& \begin{array}{l}{a}_4={\left(-1\right)}^4\cdot 3\left(4\right)\\ =1\cdot 12\\ =12\end{array}& \begin{array}{l}{a}_5={\left(-1\right)}^5\cdot 3\left(5\right)\\ =-1\cdot 15\\ =-15\end{array}\end{array}$

Step 3. Conclusion

From the above step, we can conclude that the first five terms of the sequence will be$-3,6,-9,12,-15.$