Question

What are the explicit equation and domain for a geometric sequence with a first term of 4 and a second term of −12

Answer 1

Answer: $a_n=4(-3)^{n-1}$

Domain: Set of Natural numbers.

Step-by-step explanation:

The general explicit equation for the nth term of a geometric sequence is:

$a_n=a_{1}r^{n-1}$, where r is the common ratio.

Given: First term =$a_1=4$

Second term =$a_2=-12$

Common Ratio=$r=\dfrac{a_2}{a_1}=\dfrac{-12}{4}=-3$

Now, the explicit equation for given geometric sequence is:

$a_n=4(-3)^{n-1}$

• The domain of the geometric sequence is always the set of natural numbers , since each term has an order which can only represent by natural number.

Answer 2

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