Question

What is the termof the sequence$\left\{a_n\right\}$if ${\mathbf{a}}_{\mathbf{n}}$equals

$\begin{array}{r}\mathbf{\left(}\mathbf{a}\mathbf{\right)}\mathbf{}\mathbf{}{\mathbf{2}}^{\mathbf{n}\mathbf{-}\mathbf{1}}\mathbf{?}\\ \mathbf{\left(}\mathbf{b}\mathbf{\right)}\mathbf{}\mathbf{7}\\ \mathbf{\left(}\mathbf{c}\mathbf{\right)}\mathbf{}\mathbf{1}\mathbf{+}\mathbf{(}\mathbf{-}\mathbf{1}{\mathbf{)}}^{\mathbf{n}}\mathbf{?}\\ \mathbf{\left(}\mathbf{d}\mathbf{\right)}\mathbf{}\mathbf{-}\mathbf{(}\mathbf{-}\mathbf{2}{\mathbf{)}}^{\mathbf{n}}\mathbf{?}\end{array}$

Short answer

Hence, the terms of the given sequence are:

(a)For the sequence $2^{\mathrm{n}-1},a_8=128$.

(b) For the sequence $7,{\mathrm{a}}_8=7$

(c) For the sequence$1+(-1{)}^n,a_8=2$

(d) For the sequence$-(-2{)}^n,a_8=-256$

Step-by-step solution

(a)Step 1: Solve for the value of n as 8 in the sequence 2n-1

We find $a_8$by substituting n = in the given sequence $2^{n-1}$.

$\begin{array}{r}{a}_8=2^{8-1}\\ =2^7\\ =128\end{array}$

(b)Step 2: Solve for the value of n as 8 in the sequence 7

The given sequence is a single number sequence and hence,

$a_8=7$

(c)Step 3: Solve for the value of n as 8 in the sequence

We find $a_8$by substituting n = 8 in the given sequence $a_n=1+(-1{)}^n$.

$\begin{array}{r}{a}_8=1+(-1{)}^8\\ =1+1\\ =2\end{array}$

(d)      Step 4: Solve for the value of n as 8 in the sequence

We find $a_8$by substituting n = 8in the given sequence ${\mathrm{a}}_{\mathrm{n}}=-{\left(-2\right)}^{\mathrm{n}}$.

$\begin{array}{r}{a}_8=-(-2{)}^8\\ =-256\end{array}$