Geometric Sequence Sequences and Series

Geometric Sequence A sequence is geometric if the ratios of consecutive terms are the same. 2, 8, 32, 128, 512,... geometric sequence The common ratio, r, is 4.

Find the common ratio of the following: 1) 1, 2, 4, 8, 16,... r = 2 2) 27, 9, 3, 1, 1/3,... r = 1/3 3) 3, 6, 12, 24, 48,... r = 2 4) 1/2, -1, 2, -4, 8,... r = -2

Write the first 6 terms of the geometric sequence with the first term of 6 and common ratio of 1/3

The nth term of a geometric sequence has the form a n = a 1 r n - 1 where r is the common ratio of consecutive terms of the sequence. 15, 75, 375, 1875,... a 1 = 1 5 The n th term is 15(5 n -1 ). a 2 = 1 5(5) a 3 = 1 5(5 2 ) a 4 = 1 5(5 3 )

Example 6 Find the 9th term of the geometric sequence 7, 21, 63,... a 1 = 7 The 9th term is 45,927. a n = a 1 r n – 1 = 7(3) n – 1 a 9 = 7(3) 9 – 1 = 7(3) 8 = 7(6561) = 45,927

Your Turn Find the 8 th term of the geometric sequence whose first term is -4 and whose common ratio is -2 a 8 = -4(-128) = 512