moparian
moparian moparian
  • 14-07-2021
  • Mathematics
contestada

{-2, 6, -18, 54.-162,...}
Can anyone please find the explicit rule and 10th term please.

Respuesta :

Wolfhound905
Wolfhound905 Wolfhound905
  • 14-07-2021

10th number is: 39366

Example of sequence:

(common ratio is found by [6/-2], [-18/6] which both give -3)

Ver imagen Wolfhound905
Answer Link
jimrgrant1 jimrgrant1
  • 14-07-2021

Answer:

see explanation

Step-by-step explanation:

There is a common ratio between consecutive terms , that is

6 ÷ - 2 = - 18 ÷ 6 = 54 ÷ - 18 = - 162 ÷ 54 = - 3

This indicates the sequence is geometric with explicit rule

[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 = - 3 , then

a₁₀ = - 2 [tex](-3)^{9}[/tex] = - 2 × - 19683 = 39366

Answer Link

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