Question

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

Answer 1

Answer:

The explicit formula  of the given sequence

$a_n=27-4n$

Step-by-step 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 ,$a_n=27-4n$.

Answer 2

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.

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