Question

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

The explicit rule for a sequence is

an= 14 − 9n .



What is the recursive rule for the sequence?

Answer 1

C

Explanation:

Generate the first few terms using the explicit rule

`a_(1)` = 14 - (9 × 1) = 14 - 9 = 5

`a_(2)` = 14 - (9 × 2) = 14 - 18 = - 4

`a_(3)` = 14 - (9 × 3) = 14 - 27 = - 13

`a_(4)` = 14 - (9 × 4) = 14 - 36 = - 22

The first 4 terms in the sequence are

5, - 4, - 13, - 22

These are the terms of an arithmetic sequence with common difference d

d = - 4 - 5 = - 13 - (- 4) = - 22 - (- 13) = - 9

To obtain the next term in the sequence subtract 9 from the previous term

`a_(n)` =
`a_(n-1)` - 9 with
`a_(1)` = 5

Answer 2

Answer:
`\bold{(C)\ a_n=a_(n-1)-9 \qquad a_1=5}`

Explanation:

The explicit rule for an arithmetic sequence is:
`a_n=a_1+d(n -1 )\ \rightarrow \ a_n=a_1 -d +dn`

The given explicit rule is:
`a_n=14 - 9n`

So, we know that d = -9 and a₁ - (-9) = 14 ⇒ a₁ = 5

The recursive rule for an arithmetic sequence is:
`a_n=a_(n-1)+d`

So, the recursive rule for the given sequence is:
`a_n=a_(n-1)-9`