# Algebra 1 : Sequences

## Example Questions

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### Example Question #7 : How To Find The Common Difference In Sequences

What is the common difference in the following sequence:

Explanation:

The common difference in this set is the linear amount spaced between each number in the set.

Subtract the first number from the second number.

Check this number by subtracting the second number from the third number.

Each spacing, or common difference is:

### Example Question #8 : How To Find The Common Difference In Sequences

What is the common difference?

Explanation:

The common difference can be determined by subtracting the first term with the second term, second term with the third term, and so forth.   The common difference must be similar between each term.

The distance between the first and second term is .

The distance between the second and third term is .

The distance between the third and fourth term is .

The fractions may seem as though they have a common difference since the denominators are increasing by one for each term, but there is no common difference among the numbers.

### Example Question #9 : How To Find The Common Difference In Sequences

What is the common difference in the following set of data?

Explanation:

In order to determine the common difference, subtract the first term from the second term.

Verify that this is the same for the difference of the third and second terms.

The set of data is increasing at increments of five.

The common difference is:

### Example Question #112 : Functions And Graphs

The product of two consective positive odd integers is 143. Find both integers.

Explanation:

If  is one odd number, then the next odd number is . If their product is 143, then the following equation is true.

Distribute into the parenthesis.

Subtract 143 from both sides.

This can be solved by factoring, or by the quadratic equation. We will use the latter.

We are told that both integers are positive, so .

The other integer is .

### Example Question #65 : Mathematical Relationships And Basic Graphs

Write a rule for the following arithmetic sequence:

Explanation:

Know that the general rule for an arithmetic sequence is

,

where  represents the first number in the sequence,  is the common difference between consecutive numbers, and  is the -th number in the sequence.

In our problem, .

Each time we move up from one number to the next, the sequence increases by 3.  Therefore,

The rule for this sequence is therefore .

### Example Question #41 : Sequences

If the rule of some particular sequence is written as

,

find the first five terms of this sequence

none of these

Explanation:

The first term for the sequence is where . Thus,

So the first term is 4.  Repeat the same thing for the second , third , fourth , and fifth  terms.

We see that the first five terms in the sequence are

### Example Question #42 : Sequences

What are three consecutive numbers that are equal to ?

Explanation:

When finding consecutive numbers assign the first number a variable.

If the first number is assigned the letter n, then the second number that is consecutive must be  and the third number must be .

Write it out as an equation and it should look like:

Simplify the equation then,

If  then

And

### Example Question #43 : Sequences

The sum of five odd consecutive numbers add to . What is the fourth largest number?

Explanation:

Let the first number be .

If  is an odd number, the next odd numbers will be:

, and

The fourth highest number would then be:

Set up an equation where the sum of all these numbers add up to .

Simplify this equation.

Subtract 20 from both sides.

Simplify both sides.

Divide by five on both sides.

Corresponding to the five numbers, the set of five consecutive numbers that add up to  are:

The fourth largest number would be .

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