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What are the explicit equation and domain for a geometric sequence with a first term of 3 and a second term of −9?

User Copas
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2 Answers

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u can find the common ratio by dividing the 2nd term by the first term
r = -9/3 = -3

an = a1 * r^(n - 1)
a1 = 1st term = 3
r = common difference = -3
now sub
an = 3 * -3^(n - 1) <== ur formula
domain : all integers where n > = 1 <==
User Luc Bloom
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8.1k points
4 votes

Answer:
\ a_(n)=3(-3)^(n-1)


Explanation:

Given: A geometric sequence with its first term
a_1=a=3

and second term
a_2=-9

We know that the common ratio in of a geometric sequence=
(a_(n))/(a_(n-1))

Thus, common ratio
r=(-9)/(3)=-3

We know that the explicit rule for geometric sequence is written as


a_(n)=ar^(n-1)\\\Rightarrow\ a_(n)=3(-3)^(n-1)..[\text{by substituting the values of 'a' and 'r' in it }]

Thus, the explicit rule for the given geometric sequence is
\ a_(n)=3(-3)^(n-1) for every n ,a natural number.

User Ngrashia
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