# SAT II Math I : Sequences

## Example Questions

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### Example Question #1 : Sequences

The first two numbers of a sequence are, in order, 1 and 4. Each successive element is formed by adding the previous two. What is the sum of the first six elements of the sequence?

Explanation:

The first six elements are as follows:

### Example Question #2 : Sequences

The first and third terms of a geometric sequence are 3 and 108, respectively. All What is the sixth term?

Insufficient information is given to answer the question.

Insufficient information is given to answer the question.

Explanation:

Let the common ratio of the sequence be . Then The first three terms of the sequence are . The third term is 108, so

or .

The common ratio can be either - not enough information exists for us to determine which.

The sixth term is

If , the seventh term is .

If , the seventh term is .

Therefore, not enough information exists to determine the sixth term of the sequence.

### Example Question #1 : Sequences

The first and third terms of a geometric sequence are 2 and 50, respectively. What is the seventh term?

Insufficient information is given to answer the question.

Explanation:

Let the common ratio of the sequence be . Then The first three terms of the sequence are . The third term is 50, so

or .

Not enough information is given to choose which one is the common ratio. But the seventh term is

If , the seventh term is .

If , the seventh term is .

Either way, the seventh term is 31,250.

# The sum of 3 odd consecutive numbers is 345. What is the largest number in the sequence?

Explanation:

When you are dealing with arithmetic means, it is best to define one number in the sequence as x and every other number relative to x.

Because we are trying to find the largest of three numbers, let's define x as the largest number in the equation. Because each number is a consecutive odd number, we must subtract 2 to get to the next number in the sequence.

x: largest number in sequence

x-2: middle number in sequence

x-4: smallest number in sequence

Now, let's make an equation finds the sum of all the numbers in the sequence and set it equal to 354.

### 117 is the largest number in the sequence.

To check yourself, you can add up the numbers in the sequence {113, 115, 117}.

### Example Question #5 : Sequences

What is the next number in the sequence?

Explanation:

The first number is multiplied by three

.

Then it is divide by two

.

The following is multiplied by three

then divided by two

.

That makes the next step to multiply by three which gives us

.

### Example Question #101 : Sat Subject Test In Math I

An arithmetic sequence begins as follows:

Give the tenth term of this sequence.

Explanation:

Rewrite the first term in fraction form: .

The sequence now begins

,...

Rewrite the terms with their least common denominator, which is :

The common difference  of the sequence is the difference of the second and first terms, which is

.

The rule for term  of an arithmetic sequence, given first term  and common difference , is

;

Setting , , and  , we can find the tenth term  by evaluating the expression:

,

the correct response.

### Example Question #1 : Sequences

A geometric sequence begins as follows:

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

Explanation:

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

The common ratio  of a geometric sequence is the quotient of the second term and the first:

Multiply the second term by the common ratio to obtain the third term:

### Example Question #1 : Sequences

The second and third terms of a geometric sequence are  and  , respectively. Give the first term.

Explanation:

The common ratio  of a geometric sequence is the quotient of the third term and the second:

Multiplying numerator and denominator by , this becomes

The second term of the sequence is equal to the first term multiplied by the common ratio:

.

so equivalently:

Substituting:

,

the correct response.

### Example Question #1 : Sequences

A geometric sequence begins as follows:

Give the next term of the sequence.

None of the other choices gives the correct response.

Explanation:

The common ratio  of a geometric sequence is the quotient of the second term and the first:

Simplify this common ratio by multiplying both numerator and denominator by :

Multiply the second term by the common ratio to obtain the third term:

### Example Question #1 : Sequences

A geometric sequence has as its first and third terms  and 24, respectively. Which of the following could be its second term?

None of these

Explanation:

Let  be the common ratio of the geometric sequence. Then

and

Therefore,

,

and

Setting :

.

Substituting for  and , either

.

The second term can be either  or , the former of which is a choice.

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