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

Correct answer only ! the explicit rule for a sequence

daiscott2306

10.03.2022

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

Step-by-step 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: $a_n=a_{n-1}-9$

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lillitzy8865

10.03.2022

Step-by-step 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

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brownvester44

13.01.2023

Because the negatives are opposite on both examples, therefore the symbols saying how one is greater than the other aren’t correct

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