Question

Write a recursive formula for the explicit formula

A(n) = -1 + (n-1)(-2)

Answer 1

see explanation

Explanation:

A recursive formula allows a term in the sequence to be found by adding a common difference to the previous term

Given the explicit formula

A(n) = - 1 + (n - 1)(- 2)

This is an arithmetic sequence with explicit formula

A(n) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

For the given explicit formula, then

a₁ = - 1 and d = - 2

The recursive formula is then

`a_(n+1)` =
`a_(n)` - 2 ; a₁ = - 1