Question

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

Answer 1

The standard form of a geometric sequence is $a_{n}=a_{1}(r)^{n-1}$. We are told that the first number in the sequence is 5 and the second number is -10. Geometric sequences rely on that r to be a common ratio which is a muliplier. So to get from 5 to -10 we have to multiply by -2. That means that r = -2. Our formula then is $a_{n}=5(-2)^{n-1}$ and any value could be subbed in for n to find that specific number in the sequence. A geometric sequence may be thought of as an exponential function whose domain is the set of natural numbers.