8 - Mount Saint Mary College



8.2b Geometric Progression

A geometric progression is a sequence of numbers in which each term after the first is obtained by multiplying the proceeding term by a constant r. The constant r is called the common ratio.

What is the nth term of a geometric progression with the first term a and common ratio r?

[pic]

[pic]

Find the 7th term of the following geometric progression whose first five terms are

3,6,12,24…

Find the eighth term of a geometric progression whose first five terms are 162,54,18,6,2...

Find the tenth term of a geometric progression whose third term is 16 and whose seventh term is 1.

Find the 15th term of the geometric sequence whose first term is 20 and whose common ratio is 1.05.

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The 4th term of a geometric sequence is 125, and 10th term is [pic]. Find the 14th term. (Assume that the terms of the sequence are positive.)

A geometric series is an infinite series in which the ratio of successive terms in the series is constant. If this contains r, then the series has the form

[pic][pic]

The sum of a geometric series can be found

[pic]

Find the first six partial sums of the series. Then use the formula to find the sum of the series.

[pic]

4) Determine if the following series converges or diverges. If it converges, find its sum.

a)[pic] b)[pic]

5) Find the sum of the geometric series

a) [pic] b) 1+0.4+0.16+0.064…..

c) [pic] d) [pic]

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