What kind of sequence is this? 114, 132, 150, 168, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Verify Consecutive Differences Uniform: Let's verify if the differences between consecutive terms are uniform. Given sequence: 114, 132, 150, 168, ... Are the consecutive differences in the sequence equal? 132 - 114 = 18, 150 - 132 = 18, 168 - 150 = 18. The consecutive differences in the sequence are equal.Identify Arithmetic Sequence: Since the consecutive differences 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: To confirm that it's not a geometric sequence, we need to check if there is a common ratio between consecutive terms. Given sequence: 114, 132, 150, 168, ... Are the ratios between consecutive terms in the sequence equal? 132 / 114 ≈ 1.158, 150 / 132 ≈ 1.136, 168 / 150 ≈ 1.12. The ratios are not equal, so it is not a geometric sequence.Confirm Arithmetic Sequence: Since the sequence has a common difference but not a common ratio, it is an arithmetic sequence and not a geometric sequence. Therefore, the correct choice is (A) arithmetic.

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What kind of sequence is this? $\newline$ $114, 132, 150, 168, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Algebra 2

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Q. What kind of sequence is this?

\newline

114, 132, 150, 168, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Verify Consecutive Differences Uniform: Let's verify if the differences between consecutive terms are uniform. Given sequence: $114, 132, 150, 168, ext{...}$ Are the consecutive differences in the sequence equal? $132 - 114 = 18$ , $150 - 132 = 18$ , $168 - 150 = 18$ . The consecutive differences in the sequence are equal.
Identify Arithmetic Sequence: Since the consecutive differences 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: To confirm that it's not a geometric sequence, we need to check if there is a common ratio between consecutive terms. Given sequence: $114, 132, 150, 168, \ldots$ Are the ratios between consecutive terms in the sequence equal? $\frac{132}{114} \approx 1.158$ , $\frac{150}{132} \approx 1.136$ , $\frac{168}{150} \approx 1.12$ . The ratios are not equal, so it is not a geometric sequence.
Confirm Arithmetic Sequence: Since the sequence has a common difference but not a common ratio, it is an arithmetic sequence and not a geometric sequence. Therefore, the correct choice is $(A)$ arithmetic.