What kind of sequence is this? 1, 9, 81, 729, ... 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: 1, 9, 81, 729, ... Are the consecutive differences in the sequence equal? 9 - 1 = 8, 81 - 9 = 72, 729 - 81 = 648. 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: 1, 9, 81, 729, ... Are the ratios between consecutive terms in the sequence equal? 9 / 1 = 9, 81 / 9 = 9, 729 / 81 = 9. Yes, the sequence has a common ratio of 9.Sequence Classification: Since the sequence does not have a common difference, it is not an arithmetic sequence. However, it does have a common ratio, which means it is a geometric sequence.

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What kind of sequence is this? $\newline$ $1, 9, 81, 729, \dots$ $\newline$ 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

1, 9, 81, 729, \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: $1, 9, 81, 729, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $9 - 1 = 8$ , $\newline$ $81 - 9 = 72$ , $\newline$ $729 - 81 = 648$ . $\newline$ 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: $1, 9, 81, 729, \ldots$ $\newline$ Are the ratios between consecutive terms in the sequence equal? $\newline$ $\frac{9}{1} = 9$ , $\newline$ $\frac{81}{9} = 9$ , $\newline$ $\frac{729}{81} = 9$ . $\newline$ Yes, the sequence has a common ratio of $9$ .
Sequence Classification: Since the sequence does not have a common difference, it is not an arithmetic sequence. However, it does have a common ratio, which means it is a geometric sequence.