What kind of sequence is this? 47, 33, 19, 5, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check for Arithmetic Sequence: Determine if the sequence is arithmetic by checking if the differences between consecutive terms are constant. Given sequence: 47, 33, 19, 5, ... Calculate the differences between consecutive terms: 33 - 47 = -14, 19 - 33 = -14, 5 - 19 = -14. The differences between consecutive terms are all equal to -14.Confirm Arithmetic Sequence: Since the differences between consecutive terms are constant, we can conclude that the sequence is an arithmetic sequence. An arithmetic sequence is defined by having a common difference between consecutive terms, which we have established as -14.Check for Geometric Sequence: To confirm that the sequence is not geometric, check if the ratios between consecutive terms are constant. Calculate the ratios between consecutive terms: 33 / 47, 19 / 33, 5 / 19. The ratios are approximately 0.7021, 0.5758, and 0.2632, respectively. Since the ratios are not equal, the sequence is not geometric.

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What kind of sequence is this? $\newline$ $47, 33, 19, 5, \dots$ $\newline$ 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

47, 33, 19, 5, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check for Arithmetic Sequence: Determine if the sequence is arithmetic by checking if the differences between consecutive terms are constant. $\newline$ Given sequence: $47, 33, 19, 5, \ldots$ $\newline$ Calculate the differences between consecutive terms: $33 - 47 = -14$ , $19 - 33 = -14$ , $5 - 19 = -14$ . $\newline$ The differences between consecutive terms are all equal to $-14$ .
Confirm Arithmetic Sequence: Since the differences between consecutive terms are constant, we can conclude that the sequence is an arithmetic sequence. $\newline$ An arithmetic sequence is defined by having a common difference between consecutive terms, which we have established as $-14$ .
Check for Geometric Sequence: To confirm that the sequence is not geometric, check if the ratios between consecutive terms are constant. $\newline$ Calculate the ratios between consecutive terms: $\frac{33}{47}$ , $\frac{19}{33}$ , $\frac{5}{19}$ . $\newline$ The ratios are approximately $0.7021$ , $0.5758$ , and $0.2632$ , respectively. $\newline$ Since the ratios are not equal, the sequence is not geometric.