Question

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

$a_n=(-1{)}^n·2n$

Short answer

The first five terms of the sequence whose general term is$a_n=(-1{)}^n·2n$are$-2,4,-6,8,-10.$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thegeneraltermisgivenas}\\ a_n={\left(-1\right)}^n\cdot 2n\\ \text{Wehavetofindthefirstfivetermsofthesequence.}\end{array}$

Step 2. Calculating the terms

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

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

Step 3. Conclusion 

From the above step, we can conclude that the first five terms of the sequence will be$-2,4,-6,8,-10.$