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What are the explicit equation and domain for a geometric sequence with a first term of 5 and a second term of −10?

an = 5(−2)n − 1; all integers where n ≥ 1
an = 5(−2)n − 1; all integers where n ≥ 0
an = 5(−15)n − 1; all integers where n ≥ 1
an = 5(−15)n − 1; all integers where n ≥ 0

Respuesta :

Answer:

[tex]a_{n} =5(-2)^{n-1}, n\geq 1[/tex]

is right.

Step-by-step explanation:

Given that in a geometric sequence the I term is 5 and second term is -10

If first term is a, then II term is ar where r is the common ratio

Hence r = II term/I term = -10/5 =-2

Using the geometric sequence formula for nth term

we have

[tex]a_{n} =ar^{n-1}[/tex]

Substitute to get nth term as

[tex]a_{n} =5(-2)^{n-1}[/tex], for all integers n>=1

Hence option A is right answer

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