What kind of sequence is this? 77, 96, 115, 134, ... 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: 77, 96, 115, 134, ... Are the consecutive differences in the sequence equal? 96 - 77 = 19, 115 - 96 = 19, 134 - 115 = 19. 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: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. 96 / 77 does not equal 115 / 96, and neither does it equal 134 / 115. Therefore, the sequence does not have a common ratio.Sequence Classification: Since the sequence has a common difference but not a common ratio, it is an arithmetic sequence and not a geometric sequence.

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What kind of sequence is this? $\newline$ $77, 96, 115, 134, \dots$ $\newline$ 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

77, 96, 115, 134, \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: $77, 96, 115, 134, \ldots$ $\newline$ Are the consecutive differences in the sequence equal? $\newline$ $96 - 77 = 19$ , $115 - 96 = 19$ , $134 - 115 = 19$ . $\newline$ 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: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. $\frac{96}{77}$ does not equal $\frac{115}{96}$ , and neither does it equal $\frac{134}{115}$ . Therefore, the sequence does not have a common ratio.
Sequence Classification: Since the sequence has a common difference but not a common ratio, it is an arithmetic sequence and not a geometric sequence.