What kind of sequence is this? 6, 30, 150, 750, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check for Arithmetic: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: 6, 30, 150, 750, ... Are the consecutive differences in the sequence equal? Let's calculate: 30 - 6 = 24, 150 - 30 = 120, 750 - 150 = 600. The consecutive differences in the sequence are not equal.Check for Geometric: Since the sequence is not arithmetic, let's check if it's geometric by finding the ratios between consecutive terms. Given sequence: 6, 30, 150, 750, ... Are the ratios between consecutive terms in the sequence equal? Let's calculate: 30 / 6 = 5, 150 / 30 = 5, 750 / 150 = 5. Yes, the sequence has a common ratio of 5.Determine Sequence Type: Now, let's determine the type of sequence based on our findings. An arithmetic sequence has a common difference between consecutive terms, while a geometric sequence has a common ratio between consecutive terms. Since we found that the sequence has a common ratio and not a common difference, it is a geometric sequence.

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What kind of sequence is this? $\newline$ $6, 30, 150, 750, \ldots$ $\newline$ 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

6, 30, 150, 750, \ldots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check for Arithmetic: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: $6, 30, 150, 750, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? Let's calculate: $\newline$ $30 - 6 = 24$ , $\newline$ $150 - 30 = 120$ , $\newline$ $750 - 150 = 600$ . $\newline$ The consecutive differences in the sequence are not equal.
Check for Geometric: Since the sequence is not arithmetic, let's check if it's geometric by finding the ratios between consecutive terms. Given sequence: $6, 30, 150, 750, \ldots$ $\newline$ Are the ratios between consecutive terms in the sequence equal? Let's calculate: $\newline$ $\frac{30}{6} = 5$ , $\newline$ $\frac{150}{30} = 5$ , $\newline$ $\frac{750}{150} = 5$ . $\newline$ Yes, the sequence has a common ratio of $5$ .
Determine Sequence Type: Now, let's determine the type of sequence based on our findings. An arithmetic sequence has a common difference between consecutive terms, while a geometric sequence has a common ratio between consecutive terms. Since we found that the sequence has a common ratio and not a common difference, it is a geometric sequence.