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Chapter 12: Q. 98 (page 825)

Can a sequence be both arithmetic and geometric? Give reasons for your answer.

Short Answer

Expert verified

Yes a sequence can be arithmetic and geometric at the same time consider a sequence 5,5,5,5,5

Step by step solution

01

Given information

We are given a sequence

02

Explanation

Yes a sequence can be both arithmetic and geometric. Consider a sequence of 5,5,5,,.....

in this the first term is 5 and the common difference is 0 Hence the sequence is arithmetic

Now at the same time the common ratio is 1 and the first term of the sequence is 5 hence the sequence is geometric also

03

Conclusion

Yes. A sequence can be both arithmetic and geometric

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Most popular questions from this chapter

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

1+2+3+...+20

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

8+12+18+27+....

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

1-34+916-2764+....

In Problems 51–60, write out each sum.

∑k=0n-12k+1
See all solutions

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