### All SAT Math Resources

## Example Questions

### Example Question #21 : Arithmetic Sequences

**Possible Answers:**

**Correct answer:**

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

So,

### Example Question #31 : Sequences

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

**Possible Answers:**

40

32

37

41

35

**Correct answer:**

35

The series is defined by n^{2} – 1 starting at n = 1. The sixth number in the series then equal to 6^{2} – 1 = 35.

### Example Question #31 : Sequences

A sequence of numbers is as follows:

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

**Possible Answers:**

1529

248

490

719

621

**Correct answer:**

621

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 #24 : Arithmetic Sequences

Find the next term of the following sequence:

**Possible Answers:**

More information is needed

**Correct answer:**

The sequence provided is arithmetic. An arithmetic sequence has a common difference between each consecutive term. In this case, the difference is ; therefore, the next term is .

You can also use a formula to find the next term of an arithmetic sequence:

where the current term and the common difference.

### Example Question #41 : Sequences

Solve each problem and decide which is the best of the choices given.

Find the sixth term in the following arithmetic sequence.

**Possible Answers:**

**Correct answer:**

First find the common difference of the sequence,

Thus there is a common difference of

between each term,

so follow that pattern for another terms, and the result is .

### Example Question #42 : Sequences

Find the missing number in the sequence:

**Possible Answers:**

**Correct answer:**

The pattern of this sequence is where represents the position of the number in the sequence.

for the first number in the sequence.

for the second number.

For the fourth term, . Therefore, .

### Example Question #43 : Sequences

An arithmetic sequence begins as follows:

Express the next term of the sequence in simplest radical form.

**Possible Answers:**

**Correct answer:**

Using the Product of Radicals principle, we can simplify the first two terms of the sequence as follows:

The common difference of an arithmetic sequence can be found by subtracting the first term from the second:

Add this to the second term to obtain the desired third term:

.

### Example Question #44 : Sequences

An arithmetic sequence begins as follows:

Give the next term of the sequence in simplest radical form.

**Possible Answers:**

None of the other choices gives the correct response.

**Correct answer:**

None of the other choices gives the correct response.

Since no perfect square integer greater than 1 divides evenly into 5 or 10, both of the first two terms of the sequence are in simplest form.

The common difference of an arithmetic sequence can be found by subtracting the first term from the second:

Setting :

Add this to the second term to obtain the desired third term:

This is not among the given choices.

### Example Question #45 : Sequences

An arithmetic sequence begins as follows:

Give the sixth term of the sequence in *decimal form*.

**Possible Answers:**

**Correct answer:**

The common difference of an arithmetic sequence can be found by subtracting the first term from the second:

Setting :

The th term of an arithmetic sequence can be derived using the formula

Setting :

The decimal equivalent of this can be found by dividing 13 by 15 as follows:

The correct choice is .

### Example Question #46 : Sequences

An arithmetic sequence begins as follows:

Give the sixth term of the sequence.

**Possible Answers:**

**Correct answer:**

Setting :

The th term of an arithmetic sequence can be derived using the formula

Setting