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

A

Step-by-step explanation:

The standard form of a explicit formula for a geometric sequence is given by:

Where n is the nth term, a is the initial term, and r is the common ratio.

We are told that the first term is 5, so a is 5.

Also, we are told that the second term is -10. To get from 5 to -10, we multiply by -2. Therefore, the common ratio r is -2.

Plugging this into the equation, we have:

(Note: The Z means the set of all integers)

We add the second part because the term number can only be positive starting at 1. For instance, we can't have the 0th term or the 1.5th term.

The answer is A.

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