# Algebra 1 : How to find the nth term of an arithmetic sequence

## Example Questions

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

The second term of an arithmetic sequence is ; the fourth term is . What is the first term?

Explanation:

The common difference between the terms is half that between the second and fourth terms - that is:

Subtract this common difference from the second term to get the first:

### Example Question #21 : Sequences

An arithmetic sequence is given by the formula .  What is the difference between  and

Explanation:

You can either calculate the vaules of  and  and subtract, or notice from the formula that each succesive number in the sequence is 3 larger than the previous

### Example Question #12 : How To Find The Nth Term Of An Arithmetic Sequence

Consider the following arithmetic sequence:

What is the term?

Explanation:

A simple way to find the  term of an arithmetic sequence is to use the formula .

Here,  is the term you are trying to find,  is the first term, and  is the common difference. For this question, the common difference is .

### Example Question #12 : 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 #31 : Sequences

What is the 11th term in the following sequence?