What kind of sequence is this? 15, 30, 60, 120, ... 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: 15, 30, 60, 120, ... Are the consecutive differences in the sequence equal? Let's calculate: 30 - 15 = 15, 60 - 30 = 30, 120 - 60 = 60. The consecutive differences in the sequence are not equal.Check Geometric Sequence: Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: 15, 30, 60, 120, ... Are the ratios between consecutive terms in the sequence equal? Let's calculate: 30 / 15 = 2, 60 / 30 = 2, 120 / 60 = 2. Yes, the sequence has a common ratio of 2.Sequence Type Conclusion: Based on the calculations: - An arithmetic sequence has a common difference between consecutive terms. - A geometric sequence has a common ratio between consecutive terms. Since the given sequence has no common difference but has a common ratio, it is a geometric sequence.

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What kind of sequence is this? $\newline$ $15, 30, 60, 120, \dots$ $\newline$ 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?

\newline

15, 30, 60, 120, \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: $15, 30, 60, 120, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? Let's calculate: $\newline$ $30 - 15 = 15$ , $\newline$ $60 - 30 = 30$ , $\newline$ $120 - 60 = 60$ . $\newline$ The consecutive differences in the sequence are not equal.
Check Geometric Sequence: Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: $15, 30, 60, 120, \ldots$ $\newline$ Are the ratios between consecutive terms in the sequence equal? Let's calculate: $\newline$ $\frac{30}{15} = 2$ , $\newline$ $\frac{60}{30} = 2$ , $\newline$ $\frac{120}{60} = 2$ . $\newline$ Yes, the sequence has a common ratio of $2$ .
Sequence Type Conclusion: Based on the calculations: $\newline$ - An arithmetic sequence has a common difference between consecutive terms. $\newline$ - A geometric sequence has a common ratio between consecutive terms. $\newline$ Since the given sequence has no common difference but has a common ratio, it is a geometric sequence.