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Chapter 12: Q 5. (page 824)

True or False: In a geometric sequence the common ratio is always a positive number.

Short Answer

Expert verified

The statement : In a geometric sequence the common ratio is always a positive number is false.

Step by step solution

01

Step 1. Given information.

We have given statement: In a geometric sequence the common ratio is always a positive number.

  • A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
02

Step 2. True or false.

The statement : In a geometric sequence the common ratio is always a positive number is false.

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Most popular questions from this chapter

Problems 17–28, write down the first five terms of each sequence.

cn=-1n+1n2

In Problems 51–66, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.

∑k=1∞514k-1

In Problems 29–36, the given pattern continues. Write down the nth term of a sequence ansuggested by the pattern.

1,-1,1,-1,1,-1,...

In Problems 61–70, express each sum using summation notation.

1-13+19-127+......+-16136

In Problems 71-82, find the sum of each sequence.

∑(k2k=014-4)
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