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Chapter 12: Q. 190 (page 1200)

In your own words, explain the difference between a geometric sequence and a geometric series.

Short Answer

Expert verified
  • A sequence of numbers where each successive number is the product of the previous number and some constant ris called a geometric sequence.
  • A geometric series is the sum of terms of a geometric sequence.

Step by step solution

01

Step 1. Given information

To determine the difference between the geometric sequence and geometric series.

02

Step 2. Geometric sequence

A sequence of numbers where each successive number is the product of the previous number and some constant r.

The nth term of geometric sequence is

an=arn-1

03

Step 3. Geometric series

A geometric series is the sum of the terms of a geometric sequence.

The nth term of the geometric series is

S=a+ar+ar2+.........

S=a1-rn1-r

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Most popular questions from this chapter

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

a1=9andr=2

Find a general term for the sequence whose first five terms are shown.

11,14,19,116,125,鈥�

Write the first five terms of the sequence whose general term isan=2n!.

Write the first five terms of the sequence where the first term is 7 and the common difference isd=-4.

Write the first five terms of the sequence whose general term isan=3n!
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