Question

$a_n={\left(-1\right)}^n{n}^2.$Write the first five terms of the sequence whose general term is

Short answer

The first five terms of the sequence with the general term as$a_n={\left(-1\right)}^n{n}^2$are -1, 4, -9, 16 and -25

Step-by-step solution

Step 1. Given information

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

Step 2. Find the first term 

$\begin{array}{l}\text{Forthefirsttermsubstitute}n=1,\\ \Rightarrow a_1={\left(-1\right)}^1\cdot 1^2\\ =-1\cdot 1\\ =-1\end{array}$

Step 3. Find the second term 

$\begin{array}{l}\text{Forthesecondtermsubstitute}n=2,\\ \Rightarrow a_2={\left(-1\right)}^2\cdot 2^2\\ =1\cdot 4\\ =4\end{array}$

Step 4. Find the third term 

$\begin{array}{l}\text{Forthethirdtermsubstitute}n=3,\\ \Rightarrow a_3={\left(-1\right)}^3\cdot 3^2\\ =-1\cdot 9\\ =-9\end{array}$

Step 5. Find the fourth term 

$\begin{array}{l}\text{Forthefourthtermsubstitute}n=4,\\ \Rightarrow a_4={\left(-1\right)}^4\cdot 4^2\\ =1\cdot 16\\ =16\end{array}$

Step 6. Find the fifth term 

$\begin{array}{l}\text{Forthefifthtermsubstitute}n=5,\\ \Rightarrow a_5={\left(-1\right)}^5\cdot 5^2\\ =-1\cdot 25\\ =-25\end{array}$