Ch. 8 – Sequences, Series, and Probability 8.3 – Geometric Sequences

Geometric sequences are always of the form an = a1 rn-1 A sequence is geometric if consecutive numbers always have the same common ratio (r). Ex: 2, 4, 8, 16, 32, … has a common ratio of 2 Ex: has a common ratio of -2/3 Geometric sequences are always of the form an = a1 rn-1 r = the common ratio The sequence will be a1, a1r, a1r2, a1r3, …, a1rn-1

Ex: Find a formula for the following geometric sequence, then find a9: 5, 15, 45, … an = a1rn-1 = 5(3)n-1 a9 = 5(3)8 = 32805 Ex: If the 4th term of a geometric sequence is 125 and the 10th term is 125/64, find the 14th term. Think about the relationship between the 10th and 4th terms!

The sum of a finite geometric sequence is: a1 = 1st term being summed n = # terms being summed r = common ratio Ex: Find the sum: n = 8, a1 = 3(0.6) = 1.8, r = 0.6

The sum of an infinite geometric sequence is: If |r| ≥ 1 , the series does not have a sum. Ex: Find the sum: Use the infinite sum formula! To find a1, evaluate for k = 1 a1 = 4(0.6)1-1 = 4(0.6)0 = 4

Find the sum of the series. 16 31.97 15.98 .03 19.98

1174 1249 6670 2141 7096 The population in Dodge City decreases by 6% yearly. If the population was 1600 in 1875, what was the population in 1880?

Find the sum of the series. 10 7.56 7.45 9.45 9.31

Find the sum of the infinite series. 65/6 -9 3/2 9 27/2