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PLEASE HELP

the recursive rule for a sequence is shown
A=an-1+9
A1=21
What is the explicit rule for this sequence?

a. An=12n-9
B. An=9n-12
C. An=12n+9
D. An=9n+12

Respuesta :

a(n) = a(n-1)+9 means that we add 9 to the previous term to get the next term. Therefore the common difference is d = 9 this sequence is arithmetic.
The first term is a(1) = 21

Plug those two values into the arithmetic formula below and simplify
a(n) = a(1) + d * [ n - 1 ]
a(n) = 21 + 9 * [ n - 1 ]
a(n) = 21 + 9*n + 9*(-1)
a(n) = 21 + 9n - 9
a(n) = 9n+12

Answer is choice D

The explicit rule for this sequence is option D. An=9n+12

Calculation of explicit rule:

Since

A=an-1+9

A1=21

Here

a(n) = a(n-1)+9

It means that we add 9 to the previous term to get the next term. so, the common difference is d = 9

Now

The first term is a(1) = 21

So,

[tex]a(n) = a(1) + d \times [ n - 1 ]\\\\a(n) = 21 + 9 \times [ n - 1 ]\\\\a(n) = 21 + 9\times n + 9\times (-1)[/tex]

a(n) = 21 + 9n - 9

a(n) = 9n+12

hence, The explicit rule for this sequence is option D. An=9n+12

Learn more about sequence here: https://brainly.com/question/21258074

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