Question

Tim is playing a game. His score in round 1 is 1.7 points, in round 2 is 5.1 points, in round 3 is 15.3 points, and it continues to increase in the same way. Is his score a geometric sequence? If so, write a recursive definition for the sequence.

Answer 1

The recursive definition for the geometric sequence is given as follows:

$a_n = 3a_{n-1}, a_1 = 1.7$

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

$a_n = a_1q^{n-1}$

In which $a_1$ is the first term.

The recursive definition of a geometric sequence is given by:

$a_n = qa_{n-1}$

In this problem, we have that the first term and the common ratio are given, respectively, by:

$a_1 = 1.7, q = \frac{15.3}{5.1} = \frac{5.1}{1.7} = 3$.

Hence the recursive definition is given by:

$a_n = 3a_{n-1}, a_1 = 1.7$

More can be learned about geometric sequences at https://brainly.com/question/11847927

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