# How to write an equation for the nth term of a geometric sequence

For sequence B, if we multiply by 6 to the first number we will get the second number. Let's examine sequence A so that we can find a formula to express its nth term.

## Find the nth term of the geometric sequence calculator

Luckily, there is a way to arrive at the th term without the need for calculating terms 1 through Let's examine sequence A so that we can find a formula to express its nth term. 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. 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. 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. This too works for any pair of consecutive numbers. The following figure gives the formula for the nth term of a geometric sequence. Geometric Sequences - nth Term Examples, solutions, videos, worksheets, games and activities to help Algebra II students learn about how to find the nth term of a geometric sequence. This notation is necessary for calculating nth terms, or an, of sequences. Mathematicians use the letter r when referring to these types of sequences. Example: Given the information about the geometric sequence, determine the formula for the nth term. How to derive the formula of a geometric sequence? The r-value can be calculated by dividing any two consecutive terms in 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.

This video shows how derive the formula to find the 'n-th' term of a geometric sequence by considering an example. If we were to try and find the 20th term, or worse the th term, it would take a long time if we were to simply multiply a number -- one at a time -- to find our terms.

### Geometric sequence formula

Scroll down the page for examples and solutions on how to use the formula. Show Step-by-step Solutions Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations. Example: Given the information about the geometric sequence, determine the formula for the nth term. This works for any pair of consecutive numbers. This also works for any pair of consecutive numbers. Finding the nth Term of a Geometric Sequence How to find any term of a geometric sequence? Mathematicians also refer to generic sequences using the letter a along with subscripts that correspond to the term numbers as follows: Generic Sequence: a1, a2, a3, a4, For sequence A, if we multiply by 2 to the first number we will get the second number. What is the formula for a Geometric Sequence? This means that if we refer to the tenth term of a certain sequence, we will label it a This video shows how derive the formula to find the 'n-th' term of a geometric sequence by considering an example. Show Step-by-step Solutions Geometric Sequences This video looks at identifying geometric sequences as well as finding the nth term of a geometric sequence. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 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.

This notation is necessary for calculating nth terms, or an, of sequences. 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.

## Finding the nth term of a geometric sequence examples

If we match each term with it's corresponding term number, we get: n. Example: Show Step-by-step Solutions Find the Formula for a Geometric Sequence Given Terms This video explains how to find the formula for the nth term of a given geometric sequence given three terms of the sequence. Sequences of numbers that follow a pattern of multiplying a fixed number from one term to the next are called geometric sequences. The r-value can be calculated by dividing any two consecutive terms in a geometric sequence. Mathematicians also refer to generic sequences using the letter a along with subscripts that correspond to the term numbers as follows: Generic Sequence: a1, a2, a3, a4, This also works for any pair of consecutive numbers. This notation is necessary for calculating nth terms, or an, of sequences. 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. If we were to try and find the 20th term, or worse the th term, it would take a long time if we were to simply multiply a number -- one at a time -- to find our terms. For sequence B, if we multiply by 6 to the first number we will get the second number. For sequence A, if we multiply by 2 to the first number we will get the second number. The third number times 6 is the fourth number: 0. Geometric Sequences - nth Term Examples, solutions, videos, worksheets, games and activities to help Algebra II students learn about how to find the nth term of a geometric sequence. Examples: 1. Mathematicians use the letter r when referring to these types of sequences.

Examples: 1. Mathematicians also refer to generic sequences using the letter a along with subscripts that correspond to the term numbers as follows: Generic Sequence: a1, a2, a3, a4, Example: Given the information about the geometric sequence, determine the formula for the nth term.

The formula for the general term for each geometric sequence is

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