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marin [14]
3 years ago
7

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

Mathematics
1 answer:
saw5 [17]3 years ago
3 0

Answer:

a_{n} = 4 (-5)^{n-1}

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 )

a_{n} = a₁ (r)^{n-1}

where a₁ is the first term and r the common ratio

Here a₁ = 4 and r = - 5 , then

a_{n} = 4 (-5)^{n-1}

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Answer:

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Step-by-step explanation:

Dependent variable is the variable that changes when the independent variable changes.

In other words, when the independent variable is varied, the dependent variable changes. The dependent variable is the effect or outcome of the manipulation of the independent variable.

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8 0
3 years ago
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
allsm [11]

The vertical asymptote of the function f(x) = 3 log(x + 3) is x = -3

Step-by-step explanation:

A symptote is a line that a curve approaches but never touches

  • The vertical asymptote of a logarithmic function is at the zero of the argument
  • f(x) = log(argument) has vertical aymptotes at  argument  = 0

∵ f(x) = 3 ㏒(x + 3)

∵ The argument is (x + 3)

- Equate the argument by zero

∵ x + 3 = 0

- Subtract 3 from both sides

∴ x = -3

- The vertical asymptote of a logarithmic function is at the zero

  of the argument

∴ The vertical asympotote of f(x) is x = -3

The vertical asymptote of the function f(x) = 3 log(x + 3) is x = -3

Learn more:

You can learn more about the logarithmic functions in brainly.com/question/11921476

#LearnwithBrainly

8 0
3 years ago
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