# SSAT Upper Level Math : Sequences and Series

## Example Questions

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### Example Question #1 : How To Find Consecutive Integers

Three consecutive even integers have sum 924. What is the product of the least and greatest of the three?

No three consecutive even integers have sum 924.

Explanation:

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

The three even integers are therefore 306, 308, and 310, and the product of the least and greatest of these is

### Example Question #2 : How To Find Consecutive Integers

Three consecutive odd integers have sum 537. What is the product of the least and greatest of the three?

Explanation:

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

The three integers are 177, 179, and 181, and the product of the least and greatest is

### Example Question #3 : How To Find Consecutive Integers

Four consecutive integers have sum 3,350. What is the product of the middle two?

Explanation:

Call the least of the four integers . The four integers are therefore

,

and they can be found using the equation

The integers are 836, 837, 838, 839.

To get the correct response, multiply:

### Example Question #1 : How To Find Consecutive Integers

Three consecutive integers have sum . What is their product?

Explanation:

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

This contradicts the condition that the numbers are integers. Therefore, three integers satisfying the given conditions cannot exist.

### Example Question #5 : How To Find Consecutive Integers

Three consecutive integers have a sum of . What is their product?

Explanation:

Let the middle integer of the three be . The three integers are therefore

, and they can be found using the equation

The integers are therefore 103, 104, 105. The correct response is their product, which is

### Example Question #6 : How To Find Consecutive Integers

What is the value of  is this sequence?

Explanation:

This is a geometric sequence since the pattern of the sequence is through multiplication.

You have to multiple each value by  to get the next one.

The value before  is  so .

### Example Question #7 : How To Find Consecutive Integers

Which of the following can be the sum of four consecutive positive integers?

None of the other answers are correct.

Explanation:

Let , and  be the four consecutive integers. Then their sum would be

In other words, if 6 were to be subtracted from their sum, the difference would be a multiple of 4. Therefore, we subtract 6 from each of the choices and see if any of the resulting differences are multiples of 4.

Since this only happens in the case of 178, this is the only number of the four that can be a sum of four consecutive integers: 43, 44, 45, 46.

### Example Question #1 : How To Find The Common Difference In Sequences

Set R consists of multiples of 4. Which of the following sets are also included within set R?

Set Z, containing multiples of 1.

Set Q, containing multiples of 7.

Set W, containing multiples of 8.

Set X, containing multiples of 2.

Set Y, containing multiples of 6.

Set W, containing multiples of 8.

Explanation:

The easiest way to solve this problem is to write out the first few numbers of the sets.

Set R (multiples of 4):

Set W (multiples of 8):

Set X (multiples of 2):

Set Y (multiples of 6):

Set Z (multiples of 1):

Set Q (multiples of 7):

Given that Set W is the only set in which the entire set of numbers is reflected in Set R, it is the correct answer.

### Example Question #2 : How To Find The Common Difference In Sequences

What number comes next in this sequence?

4   12   9   6   18   15   12   36   33   __

Explanation:

Determining sequences can take some trial and error, but generally aren't as intimidating as they may at first appear. For this sequence, you multiply the first term by 3, and then subtract 3 two times in a row. Then repeat. When you get to 33, you have only subtracted 3 once, so you have to do that one more time:

### Example Question #3 : How To Find The Common Difference In Sequences

What number comes next in the sequence?

_______