What kind of sequence is this? 100, 82, 64, 46, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: 100, 82, 64, 46, ... Are the consecutive differences in the sequence equal? 82 - 100 = -18, 64 - 82 = -18, 46 - 64 = -18. The consecutive differences in the sequence are equal.Identify Arithmetic Sequence: Since the differences between consecutive terms are equal, this indicates that the sequence is an arithmetic sequence. An arithmetic sequence is defined by having a common difference between consecutive terms.Check for Geometric Sequence: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. Given sequence: 100, 82, 64, 46, ... Are the ratios between consecutive terms in the sequence equal? 82 / 100 = 0.82, 64 / 82 ≈ 0.7805, 46 / 64 ≈ 0.71875. The ratios between consecutive terms are not equal.Conclude Not Geometric Sequence: Since the sequence does not have a common ratio, it is not a geometric sequence. A geometric sequence is defined by having a common ratio between consecutive terms.

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What kind of sequence is this? $\newline$ $100, 82, 64, 46, \dots$ $\newline$ 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

100, 82, 64, 46, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: $100, 82, 64, 46, \ldots$ Are the consecutive differences in the sequence equal? $82 - 100 = -18$ , $64 - 82 = -18$ , $46 - 64 = -18$ . The consecutive differences in the sequence are equal.
Identify Arithmetic Sequence: Since the differences between consecutive terms are equal, this indicates that the sequence is an arithmetic sequence. An arithmetic sequence is defined by having a common difference between consecutive terms.
Check for Geometric Sequence: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. Given sequence: $100, 82, 64, 46, \ldots$ Are the ratios between consecutive terms in the sequence equal? $\frac{82}{100} = 0.82$ , $\frac{64}{82} \approx 0.7805$ , $\frac{46}{64} \approx 0.71875$ . The ratios between consecutive terms are not equal.
Conclude Not Geometric Sequence: Since the sequence does not have a common ratio, it is not a geometric sequence. A geometric sequence is defined by having a common ratio between consecutive terms.