ginac21389
Answered

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Write an explicit formula for a_n, the nth term of the sequence 4, -20, 100, ...

Sagot :

Answer:

[tex]a_{n}[/tex] = 4 [tex](-5)^{n-1}[/tex]

Step-by-step explanation:

There is a common ratio r between consecutive terms , that is

r = - 20 ÷ 4 = 100 ÷ - 20 = - 5

This indicates the sequence is geometric with nth term ( explicit formula )

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

where a₁ is the first term and r the common ratio

Here a₁ = 4 and r = - 5 , then

[tex]a_{n}[/tex] = 4 [tex](-5)^{n-1}[/tex]

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