Chapter 4.7, Problem 44PPE

To determine

Tofind:a recursive formula for the explicit formula $A\left(n\right)=-1+\left(n-1\right)\left(-2\right)$ .

Answer to Problem 44PPE

  $A\left(n\right)=A\left(n-1\right)-2;A\left(1\right)=-1$

Explanation of Solution

Given information:

The explicit formula for the sequence is $A\left(n\right)=-1+\left(n-1\right)\left(-2\right)$

Calculation:

We know that the explicit formula for the arithmetic sequence with first term $A\left(1\right)$ and common ratio d is

  $A\left(n\right)=A\left(1\right)+\left(n-1\right)\left(d\right)$

Therefore, the first term of given sequence is $A\left(1\right)=-1$ and common ratio is $d=-2$ .

Now, the recursive formula for the arithmetic sequence with first term $A\left(1\right)$ and common ratio d is

  $A\left(n\right)=A\left(n-1\right)+d$

Thus, recursive formula for given sequence is

  $A\left(n\right)=A\left(n-1\right)-2;A\left(1\right)=-1$