peterradu7576 peterradu7576
  • 22-04-2020
  • Mathematics
contestada

Given a term in a geometric sequence and the common ratio, find the explicit formula, a11=5120 ans r=-2

Respuesta :

Newton9022 Newton9022
  • 26-04-2020

Answer:

[tex]U_n=5(-2)^{n-1}[/tex]

Step-by-step explanation:

Given a geometric sequence, the nth term of the geometric sequence is obtained by using the formula:

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

If the eleventh term, [tex]a_{11}=5120[/tex]

and the common ratio, r=-2.

Then:

[tex]5120=a(-2)^{11-1}\\a=\frac{5120}{2^{10}} =5[/tex]

The explicit formula for the sequence is:

[tex]U_n=5(-2)^{n-1}[/tex]

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