avahall19 avahall19
  • 01-06-2021
  • Mathematics
contestada

Find an explicit rule for the nth term of the sequence.

-2, -8, -32, -128

Respuesta :

jimrgrant1 jimrgrant1
  • 01-06-2021

Answer:

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

Step-by-step explanation:

There is a common ratio between consecutive terms , that is

r = - 8 ÷ - 2 = - 32 ÷ - 8 = - 128 ÷ - 32 = 4

This indicates the sequence is geometric with nth term

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = - 2 and r = 4 , then explicit formula is

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

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