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Which of the following is the explicit rule for a geometric sequence defined by a recursive formula of an=5an-1 for which the first term is 23?

Which of the following is the explicit rule for a geometric sequence defined by a recursive formula of an=5an-1 for which the first term is 23? class=

Answer :

Answer:

D

Step-by-step explanation:

The explicit rule for a geometric sequence is

[tex]a_{n}[/tex] = a [tex]r^{n-1}[/tex]

where a is the first term and r the common ratio

Here a = 23 and from the recursive formula

[tex]a_{n}[/tex] = 5[tex]a_{n-1}[/tex] , then r = 5 , thus explicit formula is

[tex]a_{n}[/tex] = 23 × [tex]5^{n-1}[/tex] → D

The correct option is D.

  • The calculation is as follows:

The explicit rule for a geometric sequence is

[tex]an = ar^{n-1}[/tex]

Here

a represents the first term

r represents the common ratio

So,

[tex]a_n = 5a_{n-1}[/tex]

So,

[tex]a_n = 23\times 5^{n-1}[/tex]

Learn more: brainly.com/question/17429689

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