Question

In Problems 1– 4, write down the first five terms of each sequence.

$\left\{a_n\right\}=\left\{{\left(-1\right)}^n\left(\frac{n+3}{n+2}\right)\right\}$

Short answer

First five term of the sequence are:$-\frac{4}{3},\frac{5}{4},-\frac{6}{5},\frac{7}{6},-\frac{8}{7}$

Step-by-step solution

Given information.

General term of the sequence:

$\left\{a_n\right\}=\left\{{\left(-1\right)}^n\left(\frac{n+3}{n+2}\right)\right\}$

Step 2. Substitute first five integral value of nin the expression an and solve.

First term is: $$\begin{gathered} a_1=\left\{{\left(-1\right)}^1\left(\frac{1+3}{1+2}\right)\right\} \\ {a}_1=-\frac{4}{3} \end{gathered}$$

Second term:$$\begin{gathered} a_2=\left\{{\left(-1\right)}^2\left(\frac{2+3}{2+2}\right)\right\} \\ {a}_2=\frac{5}{4} \end{gathered}$$

Third term: $$\begin{gathered} a_3=\left\{{\left(-1\right)}^3\left(\frac{3+3}{3+2}\right)\right\} \\ {a}_3=-\frac{6}{5} \end{gathered}$$

Fourth term: $$\begin{gathered} a_4=\left\{{\left(-1\right)}^4\left(\frac{4+3}{4+2}\right)\right\} \\ {a}_4=\frac{7}{6} \end{gathered}$$

Fifth term: $$\begin{gathered} a_5=\left\{{\left(-1\right)}^5\left(\frac{5+3}{5+2}\right)\right\} \\ {a}_5=-\frac{8}{7} \end{gathered}$$