What kind of sequence is this? 78, 156, 312, 624, ... 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: 78, 156, 312, 624, ... Are the consecutive differences in the sequence equal? 156 - 78 = 78, 312 - 156 = 156, 624 - 312 = 312.Analyzing Differences: Now, let's analyze the differences we found. The differences are: 78, 156, 312. We notice that each difference is double the previous one. This means that the differences are not constant, and therefore, the sequence is not arithmetic.Check Geometric Sequence: Next, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: 78, 156, 312, 624, ... Are the ratios between consecutive terms in the sequence equal? 156 / 78 = 2, 312 / 156 = 2, 624 / 312 = 2.Common Ratio Found: The ratios between consecutive terms are all equal to 2. This indicates that the sequence has a common ratio, which is characteristic of a geometric sequence.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What kind of sequence is this? $\newline$ $78, 156, 312, 624, \dots$ $\newline$ 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

78, 156, 312, 624, \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: $78, 156, 312, 624, ...$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $156 - 78 = 78$ , $\newline$ $312 - 156 = 156$ , $\newline$ $624 - 312 = 312$ .
Analyzing Differences: Now, let's analyze the differences we found. The differences are: $78$ , $156$ , $312$ . We notice that each difference is double the previous one. This means that the differences are not constant, and therefore, the sequence is not arithmetic.
Check Geometric Sequence: Next, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: $78, 156, 312, 624, ...$ $\newline$ Are the ratios between consecutive terms in the sequence equal? $\newline$ $\frac{156}{78} = 2$ , $\newline$ $\frac{312}{156} = 2$ , $\newline$ $\frac{624}{312} = 2$ .
Common Ratio Found: The ratios between consecutive terms are all equal to $2$ . This indicates that the sequence has a common ratio, which is characteristic of a geometric sequence.