What is the function that represents a geometric sequence among the given options?
Among the options given, f(n) = 4 × (-8)^n is the function that represents a geometric sequence. This function follows the multiplication rule of a geometric sequence. Option 3.
Understanding Geometric Sequences
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the ratio.
In the given options, a geometric sequence can be represented by the geometric function f(n) = 4 × (-8)^n. The base of the exponent in this function, -8, is the fixed ratio that defines a geometric sequence.
Option 1: f(n) = 7n + 84
This function does not exhibit the characteristic of a geometric sequence as it involves addition rather than multiplication. Therefore, it is not a geometric sequence.
Option 2: f(n) = -3n^2 + 10
Similarly, this function includes squared terms and addition, not following the multiplication rule of a geometric sequence. It is not a geometric sequence.
Option 4: f(n) = 5n + 5
This function, like the previous ones, involves addition and does not exhibit the multiplicative nature of geometric sequences. Hence, it is not a geometric sequence.
Therefore, the correct answer is option 3, f(n) = 4 × (-8)^n, as it is the only function among the options that represents a geometric sequence.