6th Grade Math Textbook, Fundamentals

 3  3  3  3  3  3  3

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13-1

So Franco will need 25 toothpicks to make the 8th shape in the pattern.

For the sequence above, you found the next term first by finding a pattern

and then by using the pattern to make a about the next term.

A conjecture is a prediction that suggests what you expect to happen.

conjecture

Arithmetic Sequences and

Geometric Sequences

Objective To recognize, describe, and extend simple patterns in sequences• To recognize and

continue a number sequence• To identify number sequences as arithmetic, geometric, or neither

• To find missing terms in a sequence

Franco used 4 toothpicks to form the first shape and
7 toothpicks to form the second shape in the pattern below.
If he continues the pattern, how many toothpicks will he
need to make the 8th shape in the pattern?

To find the number of toothpicks, list the sequencefor the number
of toothpicks used to make each shape. Then identify and extend
the pattern.

A is a list of numbers in a specific order. A sequence

may or may not follow a pattern. Each number in the sequence

is a called a.

An is a sequence of numbers that follow

a pattern. Each term is found by adding a fixed number from

one term to the next. This fixed number is called the

. It is the difference between each pair of consecutive
numbers in the sequence.

In order to determine if a sequence is an arithmetic sequence,

examine the consecutive terms. If all consecutive terms have a

constant difference, the sequence is arithmetic.

4, 7, 10, 13

7  4  3 10  7  3 13  10  3

The difference, d, is always 3, so the sequence is arithmetic.

The pattern rule is: Start at 4, and add 3 repeatedly.

To find the 8th shape in the pattern, add 3 to each succeeding term.

13  3  16 16  3  19 19  3  22 22  3  25

4, 7, 10, 13, 16, 19, 22, 25

constant

arithmetic sequence

sequence

difference

term

The constant difference of an

arithmetic sequence can be a

positive or negative number.

Think

The constant difference is 3.