What kind of sequence is this? 115, 102, 89, 76, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Differences Uniform: Step 1: Check if the differences between consecutive terms are uniform. Given sequence: 115, 102, 89, 76, ... Calculate the differences: 102 - 115 = -13, 89 - 102 = -13, 76 - 89 = -13. Arithmetic Sequence Check: Step 2: Since the differences between consecutive terms are equal, this suggests it might be an arithmetic sequence. Check if it fits the definition of an arithmetic sequence where each term after the first is obtained by adding a constant difference to the preceding term. Geometric Sequence Verification: Step 3: Verify if the sequence could also be geometric by checking if the ratios between consecutive terms are equal. Calculate the ratios: 102 / 115 ≈ 0.88696, 89 / 102 ≈ 0.87255, 76 / 89 ≈ 0.85393. The ratios are not equal.

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What kind of sequence is this? $\newline$ $115, 102, 89, 76, \dots$ $\newline$ 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

115, 102, 89, 76, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Differences Uniform: Step $1$ : Check if the differences between consecutive terms are uniform. Given sequence: $115, 102, 89, 76, ext{...}$ Calculate the differences: $102 - 115 = -13$ , $89 - 102 = -13$ , $76 - 89 = -13$ .
Arithmetic Sequence Check: Step $2$ : Since the differences between consecutive terms are equal, this suggests it might be an arithmetic sequence. Check if it fits the definition of an arithmetic sequence where each term after the first is obtained by adding a constant difference to the preceding term.
Geometric Sequence Verification: Step $3$ : Verify if the sequence could also be geometric by checking if the ratios between consecutive terms are equal. Calculate the ratios: $\frac{102}{115} \approx 0.88696$ , $\frac{89}{102} \approx 0.87255$ , $\frac{76}{89} \approx 0.85393$ . The ratios are not equal.