10.2 Arithmetic Sequences and Series

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Presentation transcript:

10.2 Arithmetic Sequences and Series

Arithmetic and Geometric Sequences An Arithmetic Sequence 3 , 6 , 9 ,12 , 15, ... + 3 A constant value is being added An Arithmetic Sequence + 3 + 3 The Common Difference (d)

3 , 6 ,12 , 24 , 48, ... Arithmetic and Geometric Sequences A constant value is being multiplied The Common Ratio (r) A Geometric Sequence ×2 ×2 ×2

Arithmetic Sequences 3 , 7 , 11 ,15 , 19, ... a₁ = 3 d = 4

Arithmetic Sequences 3 , 7 , 11 ,15 , 19, ... a₁ = 3 = 7 = 11

Arithmetic Sequences 3 , 7 , 11 ,15 , 19, ... a8= a₁ +7d =31 3 +7(4) a16= 3 +15(4) a₁ +15d =63 an = a₁ + (n –1) d

Write an equation for the nth term Arithmetic Sequences 3 , 7 , 11 ,15 , 19, ... Write an equation for the nth term an = a₁ + (n –1) d an = -1 + 4n an = 3 + 4n – 4 an = 3 + (n – 1) (4)

Find the arithmetic means in the sequence Arithmetic Sequences -2 , .... , .... , .... , 18 Find the arithmetic means in the sequence a5 = a₁+4d a1 a5 18 = -2+4d d = 5 20 = 4d

Arithmetic Sequences -2 , .... , .... , .... , 18 3 8 13 + 5 + 5 + 5

The sum of the first n terms is called the partial sum Arithmetic Series 3 +7 +11+15 +19+ ... 3 , 7 , 11 ,15 , 19, ... The sum of the first n terms is called the partial sum

Arithmetic Series To find the partial sum Use Or

Arithmetic Series Sigma Notation Last value of k nth term First value of k

Arithmetic Series