The common ratio is multiplied by the first term once to find the second term, twice to find the third term, three times to find the fourth term, and so on. įind the common ratio using the given fourth term.įind the second term by multiplying the first term by the common ratio. The sequence can be written in terms of the initial term and the common ratio. Given a geometric sequence with and, find.
The term of a geometric sequence is given by the explicit formula:Ĥ Writing Terms of Geometric Sequences Using the Explicit Formula The graph of the sequence is shown in Figure 3.Įxplicit Formula for a Geometric Sequence This is a geometric sequence with a common ratio of 2 and an exponential function with a base of 2.
Because a geometric sequence is an exponential function whose domain is the set of positive integers, and the common ratio is the base of the function, we can write explicit formulas that allow us to find particular terms.
