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Starter. Find the next 3 terms of the sequence: 2, 5, 8, 11, … 2, 6, 18, 54 4n – 2 -5n + 3. 14, 17, 20. 162, 486, 1458. 2, 6, 10. -2, -7, -12. Note 3: Arithmetic Sequences. The formula for an arithmetic sequence is:. u n = u 1 + (n – 1)d. u 1 = first term

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Starter

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  1. Starter Find the next 3 terms of the sequence: 2, 5, 8, 11, … 2, 6, 18, 54 4n – 2 -5n + 3 14, 17, 20 162, 486, 1458 2, 6, 10 -2, -7, -12

  2. Note 3: Arithmetic Sequences The formula for an arithmetic sequence is: un = u1 + (n – 1)d u1 = first term d = common difference = un+1 - un un = the nth term • An arithmetic sequence is where a number is added to get the next term • The number is called the common difference

  3. Example 1 u1 = d = 2 4 un = u1 + (n – 1)d u24 = 2 + (24 – 1)4 = 94 Calculate the 24th term in the arithmetic sequence 2, 6, 10, 14, …

  4. Sometimes you may not be asked for a term, but other parts of the formula, requiring rearranging and solving: u1 = d = 2 2 un = u1 + (n – 1)d 644 = 2 + (n – 1)x2 644 = 2 + 2n - 2 644 = 2n n = 322 Example 2 In the sequence 2, 4, 6, 8,….what is term 644?

  5. Example 3 u1 = d = 5 4 un = u1 + (n – 1)d un = 5 + (n – 1)4 = 5 + 4n - 4 = 4n + 1 Find the formula for the nth term of the sequence 5, 9, 13, 17, …

  6. Page 436 Exercise 14C Q 1-6

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