Chapter 8.1, Problem 52E

To determine

To write an expression for the apparent $n$ th term of the aequence.

Answer to Problem 52E

The apparent $n$ th term of the sequence is $a_n={\left(-1\right)}^{n+1}$

Explanation of Solution

Given information:

Given sequence

  $1,-1,1,-1,1,\mathrm{...}$

Calculation:

The given sequence can be written as,

  ${\left(-1\right)}^{1+1},{\left(-1\right)}^{2+1},{\left(-1\right)}^{3+1},{\left(-1\right)}^{4+1},{\left(-1\right)}^{5+1},\mathrm{...}$

From the above simplification, the expression for $n^{th}$ term is,

  $a_n={\left(-1\right)}^{n+1}$