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This is a lesson/slideshow presentation I made for my 8th grade PreAlgebra students.
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Algebraic SequencesPart C
Obj: Determine a specific term of a Obj: Determine a specific term of a given sequence.given sequence.
Example 1Find the 25th term in the sequence 7, 19, 31, 43, 55…
Position 0 1 2 3 4 5Term
Step 1: Find the expression for the sequence
7 19 31 43 55
n +12 -5Difference Zero Term
+12-12
-5
ALSO
12n - 5
Example 1 (continued)Find the 25th term in the sequence 7, 19, 31, 43, 55…
Position 0 1 2 3 4 5 … 25Term …
Step 2: Find the 25th term using the expression 12n - 5
7 19 31 43 55-5 295
12n – 5 12(25) – 5
300 – 5 = 295
To find the 25th term in the sequence,
substitute 25 for n.
Example 2Find the 40th term in the sequence 6, 13, 20, 27, 34…
Position 0 1 2 3 4 5Term
Step 1: Find the expression for the sequence
6 13 20 27 34
n + 7 -1Difference Zero Term
+7 -7
-1
ALSO
7n - 1
Example 2 (continued)Find the 40th term in the sequence 6, 13, 20, 27, 34…
Position 0 1 2 3 4 5 … 25Term …
Step 2: Find the 40th term using the expression 7n - 1
6 13 20 27 34-1 279
7n – 17(40) – 1
280 – 1 = 279
To find the 40th term in the sequence,
substitute 40 for n.
Practice• Find the 30th term in the sequence
-12, -18, -24, -30, -36• -6n – 6 • -186• Find the 100th term in the sequence
-24, -12, 0, 12, 24• 12n – 36• 1164
Making a Table
Hours Worked
1 2 3 4 5 6
Wages10.5
0
A mechanic is paid $10.50 per hour
For the given situation, make a table that shows at least six entries. State a rule for the situation.
21.00
31.50
42.0052.5063.00
10.50 x 2 =
10.50 x 3 =
10.50 x 4 =
10.50 x 5 =
10.50 x 6 =
21.00
31.50
42.00
52.50
63.00
Making a Table
Hours Worked
1 2 3 4 5 6
Wages10.5
0
A mechanic is paid $10.50 per hour
For the given situation, make a table that shows at least six entries. State a rule for the situation.
21.00
31.50
42.0052.5063.00
10.50 x 2
Rule:Wages = $10.50 x hours worked
Making a Table
Rope 1 10 15 20 25 30 35
Rope 2 40
Two ropes are tied together to form a rope 50m long
For the given situation, make a table that shows at least six entries. State a rule for the situation.
35 30 25 20 15
10 + n = 50
15 + n = 50
20 + n = 50
25 + n = 50
30 + n = 50
n = 40
n = 35
n = 30
n = 25
n = 20
35 + n = 50 n = 15
Making a Table
Rope 1 10 15 20 25 30 35
Rope 2 40
Two ropes are tied together to form a rope 50m long
For the given situation, make a table that shows at least six entries. State a rule for the situation.
35 30 25 20 15
Rule:Rope 1 + Rope 2 = 50
