Question

Write the first five terms of the sequence whose general term is$a_n={\left(-1\right)}^{n+1}{n}^3$

Short answer

The first five terms of the sequence with the general term as$a_n={\left(-1\right)}^{n+1}{n}^3$are 1, -8, 27, -64 and 125

Step-by-step solution

Step 1. Given information

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

Step 2. Calculating the terms

$\begin{array}{llllll}n& 1& 2& 3& 4& 5\\ a_n& \begin{array}{l}{a}_1={\left(-1\right)}^{1+1}\cdot 1^3\\ ={\left(-1\right)}^2\cdot 1\\ =1\cdot 1\\ =1\end{array}& \begin{array}{l}{a}_2={\left(-1\right)}^{2+1}\cdot 2^3\\ ={\left(-1\right)}^3\cdot 8\\ =-1\cdot 8\\ =-8\end{array}& \begin{array}{l}{a}_3={\left(-1\right)}^{3+1}\cdot 3^3\\ ={\left(-1\right)}^4\cdot 27\\ =1\cdot 27\\ =27\end{array}& \begin{array}{l}{a}_4={\left(-1\right)}^{4+1}\cdot 4^3\\ ={\left(-1\right)}^5\cdot 64\\ =-1\cdot 64\\ =-64\end{array}& \begin{array}{l}{a}_5={\left(-1\right)}^{5+1}\cdot 5^3\\ ={\left(-1\right)}^6\cdot 125\\ =1\cdot 125\\ =125\end{array}\end{array}$