Sequences The TermtoTerm Rule Here is a list

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Sequences The Term-to-Term Rule Here is a list of numbers 3, 6, 12, 24,

Sequences The Term-to-Term Rule Here is a list of numbers 3, 6, 12, 24, 48 What is the rule for going from one term to the next? That’s right – double it!

Now try to find rules for these sequences of numbers: 1, 4, 7, 10,

Now try to find rules for these sequences of numbers: 1, 4, 7, 10, 13 66, 56, 46, 36, 26 200, 100, 50, 25, 12. 5 1, 3, 7, 15, 31 5, 1, -3, -7, -11 2, -4, 8, -16, 32

The answers are: 1, 4, 7, 10, 13 Add 3 66, 56, 46, 36,

The answers are: 1, 4, 7, 10, 13 Add 3 66, 56, 46, 36, 26 Subtract 10 200, 100, 50, 25, 12. 5 Divide by 2 (halve it) 1, 3, 7, 15, 31 Double, then add 1 5, 1, -3, -7, -11 Subtract 4 2, -4, 8, -16, 32 Multiply by -2 (tricky one, that!)

SEQUENCES THE POSITION-TO-TERM FORMULA Look at this formula: t = 2 n + 3

SEQUENCES THE POSITION-TO-TERM FORMULA Look at this formula: t = 2 n + 3 What do the letters stand for? t stands for the value of a particular term n stands for the position of that term See how the formula leads to the sequence 5, 7, 9, 11, 13. . . . (n =1, 2, 3, 4, 5, . . . )

For the first number in the sequence, n = 1 So the first term

For the first number in the sequence, n = 1 So the first term is (2 x 1) + 3, which is 5 For the second number in the sequence, n = 2 So the second term is (2 x 2) + 3, which is 7 Check the other three terms shown Question: What would the tenth term in the sequence be? The answer is 23, because (2 x 10) +3 = 23 Question: What would the hundredth term in the sequence be? The answer is 203, because (2 x 100) + 3 = 203

Now see if you can find the first 5 terms for each of these

Now see if you can find the first 5 terms for each of these sequences: t = 3 n – 1 t = 5 n t=n+6 t = 4 n + 2 t = 10 n – 9 t = ½n

The answers are: t = 3 n – 1 2, 5, 8, 11, 14.

The answers are: t = 3 n – 1 2, 5, 8, 11, 14. . . t = 5 n 5, 10, 15, 20, 25. . . t=n+6 7, 8, 9, 10, 11. . . t = 4 n + 2 6, 10, 14, 18, 22. . . t = 10 n – 9 1, 11, 21, 31, 41. . . t = ½n ½, 1, 1 ½, 2, 2 ½. . .