What kind of sequence is this? 28, 84, 252, 756, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Arithmetic Sequence: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: 28, 84, 252, 756, ... Calculate the differences: 84 - 28 = 56, 252 - 84 = 168, 756 - 252 = 504. Check if the differences are equal: 56 ≠ 168 ≠ 504.Calculate Differences: Since the differences are not equal, the sequence is not arithmetic. Now, let's check if it's a geometric sequence by finding the ratios between consecutive terms. Calculate the ratios: 84 / 28 = 3, 252 / 84 = 3, 756 / 252 = 3. Check if the ratios are equal: 3 = 3 = 3.Check Geometric Sequence: The ratios between consecutive terms are equal, which means the sequence has a common ratio. Therefore, 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? $\newline$ $28, 84, 252, 756, \dots$ $\newline$ 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, 84, 252, 756, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Arithmetic Sequence: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: $28, 84, 252, 756, \ldots$ $\newline$ Calculate the differences: $84 - 28 = 56$ , $252 - 84 = 168$ , $756 - 252 = 504$ . $\newline$ Check if the differences are equal: $56 \neq 168 \neq 504$ .
Calculate Differences: Since the differences are not equal, the sequence is not arithmetic. Now, let's check if it's a geometric sequence by finding the ratios between consecutive terms. $\newline$ Calculate the ratios: $\frac{84}{28} = 3$ , $\frac{252}{84} = 3$ , $\frac{756}{252} = 3$ . $\newline$ Check if the ratios are equal: $3 = 3 = 3$ .
Check Geometric Sequence: The ratios between consecutive terms are equal, which means the sequence has a common ratio. Therefore, the sequence is geometric.