What kind of sequence is this? 28, 46, 64, 82, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Verify Differences Uniform: Let's verify if the differences between consecutive terms are uniform. Given sequence: 28, 46, 64, 82, ... Are the consecutive differences in the sequence equal? Let's calculate: 46 - 28 = 18, 64 - 46 = 18, 82 - 64 = 18. The consecutive differences in the sequence are equal.Consecutive Differences Equal: Since the consecutive differences are equal, this indicates that the sequence is an arithmetic sequence. An arithmetic sequence is defined by having a common difference between consecutive terms.Check for Geometric Sequence: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms: 46 / 28 is not equal to 64 / 46, and neither is equal to 82 / 64. Therefore, the sequence does not have a common ratio and is not a geometric sequence.Arithmetic Sequence Identified: Based on the calculations and definitions: Arithmetic sequence: Consecutive terms have a common difference. Geometric sequence: Consecutive terms have a common ratio. Since the sequence has a common difference but not a common ratio, it is an arithmetic sequence.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What kind of sequence is this? $\newline$ $28$ , $46$ , $64$ , $82$ , $\dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

View step-by-step help

Home

Math Problems

Algebra 2

Classify formulas and sequences

Full solution

Q. What kind of sequence is this?

\newline

28

46

64

82

\dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Verify Differences Uniform: Let's verify if the differences between consecutive terms are uniform. Given sequence: $28, 46, 64, 82, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? Let's calculate: $\newline$ $46 - 28 = 18$ , $\newline$ $64 - 46 = 18$ , $\newline$ $82 - 64 = 18$ . $\newline$ The consecutive differences in the sequence are equal.
Consecutive Differences Equal: Since the consecutive differences are equal, this indicates that the sequence is an arithmetic sequence. An arithmetic sequence is defined by having a common difference between consecutive terms.
Check for Geometric Sequence: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms: $\newline$ $\frac{46}{28}$ is not equal to $\frac{64}{46}$ , and neither is equal to $\frac{82}{64}$ . $\newline$ Therefore, the sequence does not have a common ratio and is not a geometric sequence.
Arithmetic Sequence Identified: Based on the calculations and definitions: $\newline$ Arithmetic sequence: Consecutive terms have a common difference. $\newline$ Geometric sequence: Consecutive terms have a common ratio. $\newline$ Since the sequence has a common difference but not a common ratio, it is an arithmetic sequence.