Geometric Sequences and series

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11.3 Geometric Sequences & Series

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Presentation transcript:

Geometric Sequences and series

A constant value is being multiplied Geometric Sequences 2 , 8 , 32 , 128 , ... × 4 × 4 × 4 A constant value is being multiplied A Geometric Sequence The Common Ratio (r)

Geometric Sequences 2 , 6 , 18 , 54 , 162 , ... a₁= 2 r = 3

Geometric Sequences 2 , 6 , 18 , 54 , 162 , ... a2 = 2 . 3 a2 = a1 . r a₁ = 2 = 6 a3 = a2 . r a3 = a1 . r 2 a3 = 6 . 3 = 18 a4 = a1 . r 3

Geometric Sequences an = a₁ . (r) n – 1 2 , 6 , 18 , 54 , 162 , ... 2 . (3) 4 =162 a10= a₁ . r 9 2 .(3)9 =39366 an = a₁ . (r) n – 1

Write an equation for the nth term Geometric Sequences 2 , 6 , 18 , 54 , 162 , ... Write an equation for the nth term an = a₁ . (r) n – 1 an = 2 . (3) n – 1

Find the geometric means in the sequence Geometric Sequences 4 , .... , .... , .... , 324 Find the geometric means in the sequence a5 = a₁. r 4 a1 a5 324 = 4 r 4 r 4 = 81 r = ±3

Or × 3 × 3 × 3 Geometric Sequences 4 , .... , .... , .... , 324 12 36 4 , .... , .... , .... , 324 12 36 108 Or × 3 × 3 × 3 4 , .... , .... , .... , 324 -12 36 -108 × -3 × -3 × -3

Geometric Series To find the partial sum Use Or