mylabgarcia11
Answered

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What is the recursive formula when given the explicit formula for the following geometric sequence?

What Is The Recursive Formula When Given The Explicit Formula For The Following Geometric Sequence class=

Sagot :

sqdancefan

Answer:

  D.  a[1] = 12; a[n] = 33·a[n-1]

Step-by-step explanation:

You can make the correct choice by seeing what you get with n=1 and n=2 in the various expressions.

In general,

  an = a1·r^(n-1)

For n=1, the value of this is ...

  a1 = a1·r^(1-1) = a1·r^0 = a1 . . . . as you expect.

That is, the a1 term of the recursive formula is the leading coefficient in the explicit formula.

__

For n=2, you have ...

  a2 = a1·r(2-1) = a1·r

That is, the previous term was multiplied by r. In the given explicit formula, r=33, so the recursive formula will tell you ...

  a[n] = 33·a[n-1]

__

Altogether, we have ...

  [tex]\boxed{a_1=12,\ a_n=33a_{n-1}}[/tex]

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