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This is a lesson/slideshow presentation I made for my 8th grade PreAlgebra students.
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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
