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# Alg2 lesson 11-3

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### Alg2 lesson 11-3

1. 1. What comes next? A geometric3, 6, 12, 24 48 96 __, __, __ sequence is a pattern ofx2 x2 x2 x2 x2 x2 numbers in Common ratio which each r=2 number is a1 = 3 found by multiplying a a2 = 6 constant by the number before a3 = 12 it.
2. 2. What’s the common ratio?8, 4, 2, 1, …r = 0.52, -6, 18, -54, … Alternating sequencer = -3
3. 3. 3, 6, 12, 24, 48, 96, … x2 x2 x2a1 = 3a2 = 6 3 x 21a3 = 12 3 x 22a4 = 24 3 x 23 an = a1 x r (n – 1)
4. 4. Write an equation for the nth term of thegeometric sequence 7, 14, 28, …. an = a1 r (n – 1) an = 7 2(n-1)Find the 80th term of the sequence an = 7 2 (n – 1) a80 = 7 279
5. 5. Complete the statement for the geometric sequence: 1536 is the ____ term of 3, 6, 12, … an = a1 r (n – 1) 1536 = 3 2 (n – 1) ____ _ 3 3 512 = 2(n – 1) 29 = 2(n – 1) 9=n–1 n = 10
6. 6. The terms between any two nonconsecutiveterms of a geometric sequence are geometricmeans.Find the three geometric means between 12 and3072. 12, ___, 192 768 3072, ..., 48 ___, ___, xr xr xr xr 12 x r4 = 3072 r4 = 256 r=4