Algebra II : Geometric Sequences

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #11 : Geometric Sequences

Find the 21st term of the sequence

[90 is 1st, so n=1]

Possible Answers:

Correct answer:

Explanation:

First, find the common ratio by dividing the second term by the first:

The nth term can be found using

,

so the 21st term is

.

Example Question #12 : Geometric Sequences

Find the 26th term of the sequence 

Possible Answers:

Correct answer:

Explanation:

First we need to find the common ratio, which we can do by dividing the second term by the first:

The first term is , the second term is , so the 26th term is

Example Question #13 : Mathematical Relationships And Basic Graphs

Find the common ratio for this geometric series:

Possible Answers:

Correct answer:

Explanation:

Find the common ratio for this geometric series:

The common ratio of a geometric series can be found by dividing any term by the term before it. More generally:

So, do try the following:

So our common ratio is 7

Example Question #11 : Mathematical Relationships And Basic Graphs

Find the next term in this geometric series:

Possible Answers:

Correct answer:

Explanation:

Find the next term in this geometric series:

to find the next term, we must first find the common ratio.

The common ratio of a geometric series can be found by dividing any term by the term before it. More generally:

So, do try the following:

So our common ratio is 7

Next, find the next term in the series by multiplying our last term by 7

Making our next term 16807

Example Question #15 : Mathematical Relationships And Basic Graphs

What is  if  and ?

Possible Answers:

Correct answer:

Explanation:

Use the geometric series summation formula.

Substitute  into , and replace the  and  terms.  The value of  is two.

Simplify the terms on the right and solve for .

Rewrite the complex fraction using a division sign.

Change the sign from division to a multiplication sign and switch the second term.

Simplify the terms inside the parentheses.

Isolate the variable by multiplying six-seventh on both sides.

Simplify both sides.

The answer is:  

Example Question #12 : Mathematical Relationships And Basic Graphs

What is the next term given the following terms?  

Possible Answers:

Correct answer:

Explanation:

Divide the second term with the first term, and the third term with the second term.

The common ratio of this geometric sequence is four.

Multiply the third term by four.

The answer is:  

Example Question #13 : Geometric Sequences

Determine the 10th term if the first term is  and the common ratio is .  Answer in scientific notation.

Possible Answers:

Correct answer:

Explanation:

Write the formula to find the n-th term for a geometric sequence.

Substitute the known values into the equation.

This fraction is equivalent to:  

The 19th term is:  

Example Question #11 : Summations And Sequences

Determine the sum:  

Possible Answers:

Correct answer:

Explanation:

Write the sum formula for a geometric series.

Identify the number of terms that exist.

There are six existing terms:  

Substitute the terms into the formula.

Simplify the complex fraction.

The sum is:  

Example Question #14 : Geometric Sequences

If the first term of a geometric sequence is 4, and the common ratio is , what is the fifth term?

Possible Answers:

Correct answer:

Explanation:

Write the formula for the n-th term of the geometric sequence.

Substitute the first term and common ratio.

The equation is:  

To find the fifth term, substitute .

The answer is:  

Example Question #2671 : Algebra Ii

Given the sequence , what is the 7th term?

Possible Answers:

Correct answer:

Explanation:

The formula for geometric sequences is defined by:  

The term  represents the first term, while  is the common ratio.  The term  represents the terms.

Substitute the known values.

To determine the seventh term, simply substitute  into the expression.

The answer is:  

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