What kind of sequence is this? 82, 100, 118, 136, ... 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: 82, 100, 118, 136, ... Calculate the differences: 100 - 82 = 18, 118 - 100 = 18, 136 - 118 = 18.Calculate Differences: Since the differences between consecutive terms are equal, this indicates that the sequence is an arithmetic sequence.Check Geometric Sequence: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. Calculate the ratios: 100 / 82, 118 / 100, 136 / 118.Calculate Ratios: Perform the calculations: 100 / 82 ≈ 1.2195, 118 / 100 = 1.18, 136 / 118 ≈ 1.1525.Sequence Type Determination: Since the ratios between consecutive terms are not equal, this indicates that the sequence is not a geometric sequence.Based on the calculations, the sequence has a common difference but not a common ratio. Therefore, it is an arithmetic sequence and not geometric.

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What kind of sequence is this? $\newline$ $82, 100, 118, 136, \dots$ $\newline$ 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

82, 100, 118, 136, \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: $82, 100, 118, 136, \ldots$ $\newline$ Calculate the differences: $100 - 82 = 18$ , $118 - 100 = 18$ , $136 - 118 = 18$ .
Calculate Differences: Since the differences between consecutive terms are equal, this indicates that the sequence is an arithmetic sequence.
Check Geometric Sequence: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. Calculate the ratios: $\frac{100}{82}$ , $\frac{118}{100}$ , $\frac{136}{118}$ .
Calculate Ratios: Perform the calculations: $100 / 82 \approx 1.2195$ , $118 / 100 = 1.18$ , $136 / 118 \approx 1.1525$ .
Sequence Type Determination: Since the ratios between consecutive terms are not equal, this indicates that the sequence is not a geometric sequence.
Sequence Type Determination: Since the ratios between consecutive terms are not equal, this indicates that the sequence is not a geometric sequence. Based on the calculations, the sequence has a common difference but not a common ratio. Therefore, it is an arithmetic sequence and not geometric.