# SAT Math : Sequences

## Example Questions

### Example Question #6 : Nth Term Of An Arithmetic Sequence

Consider the following sequence of numbers:

What will be the 8th term in the sequence?

49

56

58

60

51

51

Explanation:

Each number in the sequence in 7 more than the number preceding it.

The equation for the terms in an arithmetic sequence is an = a1 + d(n-1), where d is the difference.

The formula for the terms in this sequence is therefore an = 2 + 7(n-1).

Plug in 8 for n to find the 8th term:

a8 = 2 + 7(8-1) = 51

### Example Question #7 : Nth Term Of An Arithmetic Sequence

Find the seventh term in the following sequence:

Explanation:

The difference between each term can be found through subtraction. For example the difference between the first and the second term can be found as follows:

One can check and see that this is the case for the other given numbers in the sequence as well.

In order to find the seventh term, expand the sequence by adding 14 to the last given number (4th number) and all of the following numbers until the 7th number in the sequence is reached.

This gives the sequence:

As seen above the seventh number in the sequence is 87 and the correct answer.

### Example Question #8 : Nth Term Of An Arithmetic Sequence

What is the tenth number in the sequence:

Explanation:

The purpose of this question is to understand the patterns of sequences.

First, an equation for the  term in the sequence must be determined ().

This is true because

will create ,

will create ,

will create ,

will create .

Then, the eqution must be applied to find the specified term. For the tenth term, the expression  must be evaluated, yielding 103.

### Example Question #1 : Nth Term Of An Arithmetic Sequence

You are given a sequence with the same difference between consecutive terms. We know it starts at  and its 3rd term is . Find its 10th term.

Explanation:

From the given information, we know , which means each consecutive difference is 3.

### Example Question #10 : Nth Term Of An Arithmetic Sequence

An arithmetic sequence begins as follows:

Give the sixteenth term of this sequence.

None of the other responses give the correct answer.

Explanation:

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

Setting  and

The th term of an arithmetic sequence  can be found by way of the formula

Setting , and  in the formula:

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

An arithmetic sequence begins as follows: 14, 27, 40...

What is the first four-digit integer in the sequence?

Explanation:

Given the first two terms  and , the common difference  is equal to the difference:

Setting :

The th term of an arithmetic sequence  can be found by way of the formula

Since we are looking for the first four-digit whole number - equivalently, the first number greater than or equal to 1,000:

Setting  and  and solving for :

Therefore, the 77th term, or , is the first element in the sequence greater than 1,000. Substituting , and   in the rule and evaluating:

,

the correct choice.

### Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

Explanation:

Each term in the sequence is one less than twice the previous term.

So,

### Example Question #2 : How To Find The Next Term In An Arithmetic Sequence

What is the next number in the following series: 0, 3, 8, 15, 24 . . . ?

37

40

35

41

32

35

Explanation:

The series is defined by n2 – 1 starting at n = 1. The sixth number in the series then equal to 62 – 1 = 35.

### Example Question #3 : How To Find The Next Term In An Arithmetic Sequence

A sequence of numbers is as follows:

What is the sum of the first seven numbers in the sequence?

719

1529

621

248

490

621

Explanation:

The pattern of the sequence is (x+1) * 2.

We have the first 5 terms, so we need terms 6 and 7:

(78+1) * 2 = 158

(158+1) * 2 = 318

3 + 8 + 18 +38 + 78 + 158 + 318 = 621

### Example Question #4 : How To Find The Next Term In An Arithmetic Sequence

Find the next term of the following sequence: