1. ©G Dear 2008 – Not to be sold/Free to use
General Mathematics
Preliminary
Basic Algebra
Find the Rule
Stage 6 - Year 11
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©G Dear 2008 – Not to be sold/Free to use

2. Tn = a + (n-1) d 7: add 4 Find the Rule 1/6 7, 11, 15, 19, . . .
The pattern is
7: add 4
Tn = a + (n-1) d
(Ctrl-A or Apple-A for Arrow Pointer)
Tn = 7 + (n-1) x 4
Tn = 7 + 4n -4
Tn = 3 + 4n

3. Tn = a + (n-1) d 27: minus 2 Find the Rule 2/6 27, 25, 23, 21, . . .
The pattern is
27: minus 2
Tn = a + (n-1) d
Tn = 27 + (n-1) x -2
Tn = n + 2
Tn = n

4. Tn = ar(n-1) 3: times 2 Find the Rule 3/6 3, 6, 12, 24, . . .
The pattern is
3: times 2
Tn = ar(n-1)
Tn = 3 x 2(n-1)
Tn = 3 x 2n x 2-1
Tn = 3 x 2n x 1/2
Tn = 3/2 x 2n

5. Tn = ar(n-1) 32: times 0.5 Find the Rule 4/6 32, 16, 8, 4, . . .
The pattern is
32: times 0.5
Tn = ar(n-1)
Tn = 32 x 0.5(n-1)
Tn = 32 x 0.5n x 0.5-1
Tn = 32 x 2n x 2
Tn = 64 x 0.5n

6. Find the Rule 5/6
Other Patterns
Tn=n2
12,
22,
32,
42, . . .
Square
Numbers 1, 4, 9,
16, . . .
Tn=2n
21,
22,
23,
24, . . . 2, 4, 8,
16, . . .

7. Find the Rule 6/6
Other Patterns
Tn=n3
13,
23,
33,
43, . . .
Cubed
Numbers 1, 8,
27,
64, . . .
Tn=3n
31,
32,
33,
34, . . . 3, 9,
27,
81, . . .