Question

An arithmetic sequence has this recursive formula: What is the explicit formula for this sequence? A. an = (–1) + (n – 7)(–4)

Answer 1

bearing in mind that an explicit form is simply the sequence written as a function of some variables, so we simply simplify and add like-terms.

`\bf a_n=(-1)+(n-7)(-4)\implies a_n=-1+(-4n+28)\implies a_n=27-4n`

Answer 2

The explicit formula of the given sequence

`a_n=27-4n`

Explanation:

Given A sequence is in an arthmetic progression

The recursive formula

`a_n=(-1)+(n-7)(-4)`

Recursive formula:It is the formula to find the value of
`n^(th)` term (
`a_n` ) of the sequence when
`(n-1)^(th)` term of the sequence is known .

Explicit formula:It is the formula to find the value of any term of the sequence when
`n^(th)` term is known.

`a_n= -1-4n+28`

By simplification

`a_n= 27-4n`

By simplification

Hence, the explicit formula ,
`a_n=27-4n`.