Correct answer only ! the explicit rule for a sequence is an= 14 − 9n . what is the recursive rule for the sequence?

C

Step-by-step explanation:

Generate the first few terms using the explicit rule

= 14 - (9 × 1) = 14 - 9 = 5

= 14 - (9 × 2) = 14 - 18 = - 4

= 14 - (9 × 3) = 14 - 27 = - 13

= 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

= - 9 with = 5

Step-by-step explanation:

The explicit rule for an arithmetic sequence is:

The given explicit rule is:

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

The recursive rule for an arithmetic sequence is:

So, the recursive rule for the given sequence is: