Algebraic Sequences Part B

Algebraic SequencesPart B

Obj: Determine the sequence of the Obj: Determine the sequence of the nnth term of an algebraic expression.th term of an algebraic expression.

Example 1Write the first five terms of the sequence

that has an nth term of 6n + 7

Position 1 2 3 4 5Term

Step 1: Build a table

Step 2Fill in the table using the position numbers.

Position 1 2 3 4 5Term

To find the first term in the sequence,

substitute 1 for n.

6n + 76(1) + 7

6 + 7 = 13

13

Step 2 (continued)Fill in the table using the position numbers.

Position 1 2 3 4 5Term

To find the second term in the sequence,

substitute 2 for n.

6n + 76(2) + 7

12 + 7 = 19

13 19

Step 2 (continued)Fill in the table using the position numbers.

Position 1 2 3 4 5Term

To find the third term in the sequence,

substitute 3 for n.

6n + 76(3) + 7

18 + 7 = 25

13 19 25

Step 2 (continued)Fill in the table using the position numbers.

Position 1 2 3 4 5Term

To find the fourth term in the sequence,

substitute 4 for n.

6n + 76(4) + 7

24 + 7 = 31

13 19 25 31

Step 2 (continued)Fill in the table using the position numbers.

Position 1 2 3 4 5Term

To find the fifth term in the sequence,

substitute 5 for n.

6n + 76(5) + 7

30 + 7 = 37

13 19 25 31 37

Example 2 – The ShortcutWrite the first five terms of the sequence

that has an nth term of -3n + 11

Position 1 2 3 4 5Term

Step 1: Build a table

Step 2: To find the first term in the sequence, substitute 1

for n.

-3n + 11-3(1) + 11-3 + 11 = 8

8

Example 2 – The ShortcutWrite the first five terms of the sequence

that has an nth term of -3n + 11

Position 1 2 3 4 5Term

Step 3: The Shortcut

-3n + 11

8

The coefficient of n is the common difference between terms.

-3 -3 -3 -3

5 -12 -4

Example 3 – The Shortcut #2Write the first five terms of the sequence

that has an nth term of -5n + 9

Position 0 1 2 3 4 5Term

Step 1: Build a table (this time include zero)

Step 2: To find the zero term in the sequence, substitute 0

for n.

-5n + 9-5(0) + 90 + 9 = 9

9

Example 2 – The ShortcutWrite the first five terms of the sequence

that has an nth term of -3n + 11

Position 0 1 2 3 4 5Term

Step 3: The Shortcut

-5n + 9

9

The coefficient of n is the common difference between terms.

-5 -5 -5 -5

4 -6-1 -11 -16

-5First five

terms