# How do you write a rule for the nth term of a geometric sequence

Sequences of numbers that follow a pattern of multiplying a fixed number from one term to the next are called geometric sequences.

Show Solution The situation can be modeled by a geometric sequence with an initial term of The r-value can be calculated by dividing any two consecutive terms in a geometric sequence.

Sequence C is a little different because it seems that we are dividing; yet to stay consistent with the theme of geometric sequences, we must think in terms of multiplication.

## How to find the common ratio of a geometric sequence given two terms

Licenses and Attributions Revision and Adaptation. For example, suppose the common ratio is 9. Estimate the number of hits in 5 weeks. This also works for any pair of consecutive numbers. Provided by: OpenStax. As with any recursive formula, the initial term must be given. This works for any pair of consecutive numbers. Authored by: Abramson, Jay et al.. Sequence C is a little different because it seems that we are dividing; yet to stay consistent with the theme of geometric sequences, we must think in terms of multiplication. Show Solution The situation can be modeled by a geometric sequence with an initial term of

The common ratio can be found by dividing the second term by the first term. Write a formula for the number of hits.

The formula for the general term for each geometric sequence is Estimate the student population in Authored by: McClure,Caren. Initially the number of hits is due to the curiosity factor. Using Recursive Formulas for Geometric Sequences A recursive formula allows us to find any term of a geometric sequence by using the previous term.

Substitute the common ratio into the recursive formula for a geometric sequence. This notation is necessary for calculating nth terms, or an, of sequences.

Calculating the nth Term In order for us to know how to obtain terms that are far down these lists of numbers, we need to develop a formula that can be used to calculate these terms.

If we had to find the th term of sequence A above, we would undertake a tedious task had we decided to multiply by two each step of the way all the way to the th term.

## How to find the common ratio of a geometric sequence given two terms

For sequence A, if we multiply by 2 to the first number we will get the second number. Each term is the product of the common ratio and the previous term. The third number times 6 is the fourth number: 0. Provided by: OpenStax. This notation is necessary for calculating nth terms, or an, of sequences. So that we can examine these sequences to greater depth, we must know that the fixed numbers that bind each sequence together are called the common ratios. Provided by: Lumen Learning. Show Solution The situation can be modeled by a geometric sequence with an initial term of Because these sequences behave according to this simple rule of multiplying a constant number to one term to get to another, they are called geometric sequences. Solve an application problem using a geometric sequence. Calculating the nth Term In order for us to know how to obtain terms that are far down these lists of numbers, we need to develop a formula that can be used to calculate these terms. This works for any pair of consecutive numbers. For example, suppose the common ratio is 9. If we had to find the th term of sequence A above, we would undertake a tedious task had we decided to multiply by two each step of the way all the way to the th term. Authored by: Abramson, Jay et al..

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