Respuesta :

altavistard
The first term, a, is 2.  The common ratio, r, is 4.  Thus,

a_(n+1) = 2(4)^(n).

Check:  What's the first term?  Let n=1.  Then we get 2(4)^1, or 8.  Is that correct?  No.

Try this instead:

a_(n) = a_0*4^(n-1).  Is this correct?    Seeking the first term (n=1), does this formula produce 2?      2*4^0 = 2*1 = 2.  YES.

The desired explicit formula is   a_(n) = a_0*4^(n-1), where n begins at 1.

The explicit formula for the geometric sequence is given by:

[tex]a_n = 2(4)^{n-1}[/tex]

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem:

  • The first term is [tex]a_1 = 2[/tex].
  • The common ratio is q = 4.

Hence, the explicit formula is:

[tex]a_n = 2(4)^{n-1}[/tex]

More can be learned about geometric sequences at https://brainly.com/question/11847927