What kind of sequence is this? 6, 24, 96, 384, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Differences: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: 6, 24, 96, 384, ... Difference between the first and second term: 24 - 6 = 18 Difference between the second and third term: 96 - 24 = 72 Difference between the third and fourth term: 384 - 96 = 288 Are these differences equal? 18 ≠ 72 ≠ 288 Since the differences are not equal, the sequence is not arithmetic.Check Ratios: Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: 6, 24, 96, 384, ... Ratio of the second term to the first term: 24 / 6 = 4 Ratio of the third term to the second term: 96 / 24 = 4 Ratio of the fourth term to the third term: 384 / 96 = 4 Are these ratios equal? Yes, the sequence has a common ratio of 4.Sequence Type: Since the sequence has a common ratio but not a common difference, we can conclude that the sequence is geometric.

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What kind of sequence is this? $\newline$ $6, 24, 96, 384, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Algebra 2

Classify formulas and sequences

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Q. What kind of sequence is this?

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6, 24, 96, 384, \dots

\newline

Choices:

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(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Differences: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. $\newline$ Given sequence: $6, 24, 96, 384, \dots$ $\newline$ Difference between the first and second term: $24 - 6 = 18$ $\newline$ Difference between the second and third term: $96 - 24 = 72$ $\newline$ Difference between the third and fourth term: $384 - 96 = 288$ $\newline$ Are these differences equal? $\newline$ $18 \neq 72 \neq 288$ $\newline$ Since the differences are not equal, the sequence is not arithmetic.
Check Ratios: Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. $\newline$ Given sequence: $6, 24, 96, 384, \dots$ $\newline$ Ratio of the second term to the first term: $\frac{24}{6} = 4$ $\newline$ Ratio of the third term to the second term: $\frac{96}{24} = 4$ $\newline$ Ratio of the fourth term to the third term: $\frac{384}{96} = 4$ $\newline$ Are these ratios equal? $\newline$ Yes, the sequence has a common ratio of $4$ .
Sequence Type: Since the sequence has a common ratio but not a common difference, we can conclude that the sequence is geometric.