What kind of sequence is this? 69, 58, 48, 39, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check for Arithmetic Sequence: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: 69, 58, 48, 39, ... Calculate the differences: 58 - 69 = -11, 48 - 58 = -10, 39 - 48 = -9.Analyze Differences: Now, let's analyze the differences. Are the differences between consecutive terms equal? -11, -10, -9. The differences are not equal; they are decreasing by 1 each time.Check for Geometric Sequence: Since the differences are not constant, the sequence is not arithmetic. Now, let's check if it's geometric by finding the ratios between consecutive terms. Calculate the ratios: 58 / 69, 48 / 58, 39 / 48. We can see that these ratios are not the same just by looking at the numbers, but let's calculate them for confirmation.Calculate Ratios: Calculate the exact ratios: 58 / 69 ≈ 0.84, 48 / 58 ≈ 0.83, 39 / 48 ≈ 0.81. These ratios are not equal.Sequence Classification: Since the sequence has neither a common difference nor a common ratio, it is neither arithmetic nor geometric.

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What kind of sequence is this? $\newline$ $69, 58, 48, 39, \dots$ $\newline$ 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

69, 58, 48, 39, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check for Arithmetic Sequence: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: $69, 58, 48, 39, \ldots$ $\newline$ Calculate the differences: $58 - 69 = -11$ , $48 - 58 = -10$ , $39 - 48 = -9$ .
Analyze Differences: Now, let's analyze the differences. Are the differences between consecutive terms equal? $-11$ , $-10$ , $-9$ . The differences are not equal; they are decreasing by $1$ each time.
Check for Geometric Sequence: Since the differences are not constant, the sequence is not arithmetic. Now, let's check if it's geometric by finding the ratios between consecutive terms. $\newline$ Calculate the ratios: $\frac{58}{69}$ , $\frac{48}{58}$ , $\frac{39}{48}$ . We can see that these ratios are not the same just by looking at the numbers, but let's calculate them for confirmation.
Calculate Ratios: Calculate the exact ratios: $\frac{58}{69} \approx 0.84$ , $\frac{48}{58} \approx 0.83$ , $\frac{39}{48} \approx 0.81$ . These ratios are not equal.
Sequence Classification: Since the sequence has neither a common difference nor a common ratio, it is neither arithmetic nor geometric.