What kind of sequence is this? 593, 593, 593, 593, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Arithmetic Sequence Check: An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant difference to the previous term. To determine if this is an arithmetic sequence, we need to check if the difference between consecutive terms is constant. 593 - 593 = 0 593 - 593 = 0 Since the difference is 0, which is constant, this sequence can be considered an arithmetic sequence.Geometric Sequence Check: A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. To determine if this is a geometric sequence, we need to check if the ratio between consecutive terms is constant. 593 / 593 = 1 593 / 593 = 1 Since the ratio is 1, which is constant, this sequence can be considered a geometric sequence.Final Conclusion: Since the sequence satisfies the conditions for both an arithmetic sequence (constant difference) and a geometric sequence (constant ratio), the correct choice is (C) both.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What kind of sequence is this? $\newline$ $593, 593, 593, 593, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

View step-by-step help

Home

Math Problems

Precalculus

Identify arithmetic and geometric series

Full solution

Q. What kind of sequence is this?

\newline

593, 593, 593, 593, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Arithmetic Sequence Check: An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant difference to the previous term. To determine if this is an arithmetic sequence, we need to check if the difference between consecutive terms is constant. $\newline$ $593 - 593 = 0$ $\newline$ $593 - 593 = 0$ $\newline$ Since the difference is $0$ , which is constant, this sequence can be considered an arithmetic sequence.
Geometric Sequence Check: A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. To determine if this is a geometric sequence, we need to check if the ratio between consecutive terms is constant. $\newline$ $\frac{593}{593} = 1$ $\newline$ $\frac{593}{593} = 1$ $\newline$ Since the ratio is $1$ , which is constant, this sequence can be considered a geometric sequence.
Final Conclusion: Since the sequence satisfies the conditions for both an arithmetic sequence (constant difference) and a geometric sequence (constant ratio), the correct choice is $(C)$ both.