# Algebra 1 : Sequences

## Example Questions

### Example Question #11 : How To Find The Nth Term Of An Arithmetic Sequence

What is the 20th term of  ?

Explanation:

Notice that every odd term is increasing at an increment of , since the numbers are  .  We will ignore these terms and concentrate on only the even terms.

The even terms are  for the second, fourth, and sixth terms respectively, which means that the numbers are a multiple of nine.

The equation that represents the terms for this sequence is:  , for  even terms since it only applies to the even terms that are divisible by nine and occurs after every two terms.

Substitute  to determine the 20th term.

### Example Question #11 : How To Find The Nth Term Of An Arithmetic Sequence

What is the 11th term in the following sequence?

Explanation:

First we need to show how this sequence is changing. Let's call the first number, and the second number , and so on.

Ok, so we have established that the sequence is shrinking by 9 each time. So now we need to calculate out to the 11th term. Starting from the first term, we need to subtract 9 ten times to get to the 11th term. So that would look like this.

### Example Question #2731 : Algebra Ii

Which of the following is an example of an arithmetic sequence?

Each of these sequences is an arithmetic sequence.

Each of these sequences is an arithmetic sequence.

Explanation:

In each case, the terms increase by the same number, so all of these sequences are arithmetic.

Each term is the result of adding 1 to the previous term. 1 is the common difference.

Each term is the result of subtracting 1 from - or, equivalently, adding  to - the previous term.  is the common difference.

The common difference is 0 in a constant sequence such as this.

Each term is the result of adding  to the previous term.  is the common difference.

### Example Question #12 : Arithmetic Series

Which of the following numbers completes the arithmetic sequence below?

{13, 25, __, 49}

Explanation:

In an arithmetic sequence the amount that the sequence grows or shrinks by on each successive term is the common difference. This is a fixed number you can get by subtracting the first term from the second.

So the sequence is adding 12 each time. Add 12 to 25 to get the third term.

So the unknown term is 37. To double check add 12 again to 37 and it should equal the fourth term, 49, which it does.

### Example Question #1 : How To Find The Common Difference In Sequences

Which of the following cannot be three consecutive terms of an arithmetic sequence?

Explanation:

In each group of numbers, compare the difference of the second and first terms to that of the third and second terms. The group in which they are unequal is the correct choice.

The last group of numbers is the correct choice.

### Example Question #1 : How To Find The Common Difference In Sequences

Consider the arithmetic sequence

If , find the common difference between consecutive terms.

Explanation:

In arithmetic sequences, the common difference is simply the value that is added to each term to produce the next term of the sequence. When solving this equation, one approach involves substituting 5 for  to find the numbers that make up this sequence. For example,

so 14 is the first term of the sequence. However, a much easier approach involves only the last two terms,  and .

The difference between these expressions is 8, so this must be the common difference between consecutive terms in the sequence.

### Example Question #1 : How To Find The Common Difference In Sequences

Find the common difference in the following arithmetic sequence.

Explanation:

An arithmetic sequence adds or subtracts a fixed amount (the common difference) to get the next term in the sequence. If you know you have an arithmetic sequence, subtract the first term from the second term to find the common difference.

### Example Question #4 : How To Find The Common Difference In Sequences

Find the common difference in the following arithmetic sequence.

Explanation:

An arithmetic sequence adds or subtracts a fixed amount (the common difference) to get the next term in the sequence. If you know you have an arithmetic sequence, subtract the first term from the second term to find the common difference.

(i.e. the sequence advances by subtracting 27)

### Example Question #5 : How To Find The Common Difference In Sequences

What is the common difference in this sequence?

Explanation:

The common difference is the distance between each number in the sequence. Notice that each number is 3 away from the previous number.

### Example Question #6 : How To Find The Common Difference In Sequences

What is the common difference in the following sequence?

Explanation:

What is the common difference in the following sequence?

Common differences are associated with arithematic sequences.

A common difference is the difference between consecutive numbers in an arithematic sequence. To find it, simply subtract the first term from the second term, or the second from the third, or so on...

See how each time we are adding 8 to get to the next term? This means our common difference is 8.