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What is the equation for a geometric sequence with a first term of 4 and a second term of −12? an = 4(−3)n − 1 an = 4(3)n − 1 an = 4(36)n − 1 an = 4(−36)n − 1

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carlosego

Answer:

Option 1  [tex]a_n = 4(-3)^{n-1}[/tex]:

Step-by-step explanation:

The geometric sequences have the following form:

[tex]a_n = a_1(r)^{n-1}[/tex]

Where [tex]a_1[/tex] is the first term in the sequence

We know that the first term is 4

Then [tex]a_1[/tex] = 4

We also know that the second term is -12

Then [tex]a_2 = -12[/tex]

We know that in geometric sequences the relationship between consecutive terms is constant. So:

r = -12/4

r = -3

Finally the general formula of this sequence is:

[tex]a_n = 4(-3)^{n-1}[/tex]   Option 1

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