What kind of sequence is this? 56, 66, 76, 86, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check for Arithmetic Sequence: Determine if the sequence is arithmetic by checking if the differences between consecutive terms are constant. Calculation: 66 - 56 = 10, 76 - 66 = 10, 86 - 76 = 10. The differences between consecutive terms are all equal to 10.Confirm Arithmetic Sequence: Since the differences between consecutive terms are constant, we can conclude that the sequence is an arithmetic sequence.Check for Geometric Sequence: To check if the sequence is also geometric, we need to see if there is a common ratio between consecutive terms. Calculation: 66 / 56, 76 / 66, 86 / 76. Let's calculate these ratios. 66 / 56 ≈ 1.1786, 76 / 66 ≈ 1.1515, 86 / 76 ≈ 1.1316. The ratios between consecutive terms are not equal.Confirm Geometric Sequence: Since the ratios between consecutive terms are not equal, the sequence is not a geometric sequence.Final Conclusion: Based on the calculations in the previous steps, we can conclude that the sequence is an arithmetic sequence but not a geometric sequence.

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What kind of sequence is this? $\newline$ $56, 66, 76, 86, \ldots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither $\newline$

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Algebra 2

Classify formulas and sequences

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Q. What kind of sequence is this?

\newline

56, 66, 76, 86, \ldots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

\newline

Check for Arithmetic Sequence: Determine if the sequence is arithmetic by checking if the differences between consecutive terms are constant. $\newline$ Calculation: $66 - 56 = 10$ , $76 - 66 = 10$ , $86 - 76 = 10$ . $\newline$ The differences between consecutive terms are all equal to $10$ .
Confirm Arithmetic Sequence: Since the differences between consecutive terms are constant, we can conclude that the sequence is an arithmetic sequence.
Check for Geometric Sequence: To check if the sequence is also geometric, we need to see if there is a common ratio between consecutive terms. $\newline$ Calculation: $\frac{66}{56}$ , $\frac{76}{66}$ , $\frac{86}{76}$ . Let's calculate these ratios. $\newline$ $\frac{66}{56} \approx 1.1786$ , $\frac{76}{66} \approx 1.1515$ , $\frac{86}{76} \approx 1.1316$ . $\newline$ The ratios between consecutive terms are not equal.
Confirm Geometric Sequence: Since the ratios between consecutive terms are not equal, the sequence is not a geometric sequence.
Final Conclusion: Based on the calculations in the previous steps, we can conclude that the sequence is an arithmetic sequence but not a geometric sequence.