What kind of sequence is this? 21, 63, 189, 567, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Arithmetic Differences: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: 21, 63, 189, 567, ... Calculate the differences: 63 - 21 = 42, 189 - 63 = 126, 567 - 189 = 378. Check if the differences are equal: 42 ≠ 126 ≠ 378. Since the differences are not equal, the sequence is not arithmetic.Calculate Ratios for Geometric Sequence: Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: 21, 63, 189, 567, ... Calculate the ratios: 63 / 21 = 3, 189 / 63 = 3, 567 / 189 = 3. Check if the ratios are equal: 3 = 3 = 3. Since the ratios are equal, the sequence 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? $\newline$ $21, 63, 189, 567, \ldots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither $\newline$

View step-by-step help

Home

Math Problems

Algebra 2

Classify formulas and sequences

Full solution

Q. What kind of sequence is this?

\newline

21, 63, 189, 567, \ldots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

\newline

Check Arithmetic Differences: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: $21, 63, 189, 567, \ldots$ $\newline$ Calculate the differences: $63 - 21 = 42$ , $189 - 63 = 126$ , $567 - 189 = 378$ . $\newline$ Check if the differences are equal: $42 \neq 126 \neq 378$ . $\newline$ Since the differences are not equal, the sequence is not arithmetic.
Calculate Ratios for Geometric Sequence: Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: $21, 63, 189, 567, \ldots$ $\newline$ Calculate the ratios: $\frac{63}{21} = 3$ , $\frac{189}{63} = 3$ , $\frac{567}{189} = 3$ . $\newline$ Check if the ratios are equal: $3 = 3 = 3$ . $\newline$ Since the ratios are equal, the sequence is geometric.