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Arithmetic Sequences 4-7

Arithmetic Sequences 4-7. Objective: The student will recognize arithmetic sequences, extend and write formulas for arithmetic sequences. S. Calahan 2008. www.presentationhelper.co.uk. vocabulary. Sequence – a set of numbers in a specific order. Terms – the numbers in the sequence

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Arithmetic Sequences 4-7

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  1. Arithmetic Sequences 4-7 Objective: The student will recognize arithmetic sequences, extend and write formulas for arithmetic sequences. S. Calahan 2008 www.presentationhelper.co.uk

  2. vocabulary Sequence – a set of numbers in a specific order. Terms – the numbers in the sequence Arithmetic sequence – if the difference between successive terms is constant. Common difference – the difference between the terms

  3. Identify Arithmetic Sequences • Determine whether the sequence is arithmetic. 1, 2, 4, 8, . . . +1 +2 +4 This is not an arithmetic sequence because the difference between terms is not constant.

  4. Arithmetic Sequence • 12 17 22 27 +5 +5 +5 +5 Since this sequence has a common difference it is an arithmetic sequence.

  5. Writing arithmetic sequences • An arithmetic sequence can be found as follows a1, a1+d, a2+d, a3+d,… 74 67 60 53 ? ? ? -7 -7 -7 -7 -7 -7 The common difference is -7

  6. 74 67 60 53 ? ? ? • Add -7 to the last term of the sequence to find the next three terms. 53, 46, 39, 32

  7. nth term of an Arithmetic Sequence • The nth term of an arithmetic sequence with first term a1 and common difference d is given by an = a1 + (n – 1)d, where n is a positive integer.

  8. Find a specific term • Find the 14th term in the arithmetic sequence 9, 17, 25, 33,… • The common difference is +8 • Use the formula for the nthterm an = a1+ (n – 1) d a1 = 9, n = 14, d = 8 a14 = 9 + (14 – 1)8 = 9 + 104 = 113

  9. Write and equation for a squence • Write an equation for the nth term of the squence, 12, 23, 34, 45, … an = a1 + (n – 1)d a1 = 12, d = 11 an = 12 + (n -1)11 an = 12 + 11n – 11 Distributive property an = 11n + 1

  10. Use the equation to solve for the 10th term an = 11n + 1 n = 10 a10 = 11(10) + 1 replace n with 10 a10 = 111

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