SAT II Math I : Sequences

Study concepts, example questions & explanations for SAT II Math I

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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?

Possible Answers:

Correct answer:

Explanation:

The first six elements are as follows:

Add them:

Example Question #2 : Sequences

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

Possible Answers:

Insufficient information is given to answer the question.

Correct answer:

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 #3 : Sequences

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

Possible Answers:

Insufficient information is given to answer the question.

Correct answer:

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.

 

Example Question #4 : Sequences

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

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

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 #6 : Sequences

An arithmetic sequence begins as follows:

Give the tenth term of this sequence.

Possible Answers:

Correct answer:

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 #7 : Sequences

A geometric sequence begins as follows:

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

Possible Answers:

Correct answer:

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 #8 : Sequences

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

Possible Answers:

Correct answer:

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 #9 : Sequences

A geometric sequence begins as follows:

Give the next term of the sequence.

Possible Answers:

None of the other choices gives the correct response.

Correct answer:

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 #10 : Sequences

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

Possible Answers:

None of these

Correct answer:

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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