What kind of sequence is this? 1, 4, 16, 64, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Sequence Analysis: To determine the type of sequence, we need to examine the relationship between consecutive terms. Let's look at the ratio of each term to the previous term to see if it's constant, which would indicate a geometric sequence. Ratio of second term to first term: 4 / 1 = 4 Ratio of third term to second term: 16 / 4 = 4 Ratio of fourth term to third term: 64 / 16 = 4Geometric Sequence Identification: Since the ratio between consecutive terms is constant and equal to 4, this indicates that the sequence is a geometric sequence. An arithmetic sequence would have a constant difference between terms, which is not the case here.Matching with Choices: Now we can match our finding with the given choices. (A) arithmetic - Incorrect, as the difference is not constant. (B) geometric - Correct, as the ratio is constant. (C) both - Incorrect, as it cannot be both arithmetic and geometric. (D) neither - Incorrect, as it is geometric.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What kind of sequence is this? $\newline$ $1, 4, 16, 64, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

View step-by-step help

Home

Math Problems

Grade 8

Identify arithmetic and geometric sequences

Full solution

Q. What kind of sequence is this?

\newline

1, 4, 16, 64, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Sequence Analysis: To determine the type of sequence, we need to examine the relationship between consecutive terms. $\newline$ Let's look at the ratio of each term to the previous term to see if it's constant, which would indicate a geometric sequence. $\newline$ Ratio of second term to first term: $\frac{4}{1} = 4$ $\newline$ Ratio of third term to second term: $\frac{16}{4} = 4$ $\newline$ Ratio of fourth term to third term: $\frac{64}{16} = 4$
Geometric Sequence Identification: Since the ratio between consecutive terms is constant and equal to $4$ , this indicates that the sequence is a geometric sequence. $\newline$ An arithmetic sequence would have a constant difference between terms, which is not the case here.
Matching with Choices: Now we can match our finding with the given choices. $\newline$ (A) arithmetic - Incorrect, as the difference is not constant. $\newline$ (B) geometric - Correct, as the ratio is constant. $\newline$ (C) both - Incorrect, as it cannot be both arithmetic and geometric. $\newline$ (D) neither - Incorrect, as it is geometric.