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

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

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 = 27 - 2n + 2 Tn = 29 - 2n

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

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

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, . . .

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, . . .