What kind of sequence is this? 14, 56, 224, 896, ... 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: 14, 56, 224, 896, ... Calculate the differences: 56 - 14 = 42, 224 - 56 = 168, 896 - 224 = 672. Check if the differences are equal: 42 ≠ 168 ≠ 672. Since the differences are not equal, the sequence is not arithmetic.Check Geometric Ratios: Next, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: 14, 56, 224, 896, ... Calculate the ratios: 56 / 14 = 4, 224 / 56 = 4, 896 / 224 = 4. Check if the ratios are equal: 4 = 4 = 4. 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? $\newline$ $14, 56, 224, 896, \dots$ $\newline$ 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

14, 56, 224, 896, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Arithmetic Differences: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. $\newline$ Given sequence: $14, 56, 224, 896, \dots$ $\newline$ Calculate the differences: $56 - 14 = 42$ , $224 - 56 = 168$ , $896 - 224 = 672$ . $\newline$ Check if the differences are equal: $42 \neq 168 \neq 672$ . $\newline$ Since the differences are not equal, the sequence is not arithmetic.
Check Geometric Ratios: Next, let's check if the sequence is geometric by finding the ratios between consecutive terms. $\newline$ Given sequence: $14, 56, 224, 896, \dots$ $\newline$ Calculate the ratios: $\frac{56}{14} = 4$ , $\frac{224}{56} = 4$ , $\frac{896}{224} = 4$ . $\newline$ Check if the ratios are equal: $4 = 4 = 4$ . $\newline$ Since the ratios are equal, the sequence is geometric.