What kind of sequence is this? 28, 22, 16, 10, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Differences for Arithmetic: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: 28, 22, 16, 10, ... Calculate the differences: 22 - 28 = -6, 16 - 22 = -6, 10 - 16 = -6.Common Difference Found: Since the differences between consecutive terms are equal, we can conclude that the sequence has a common difference of -6.Check Ratios for Geometric: An arithmetic sequence is defined by having a constant difference between consecutive terms. Since we have found a common difference, this sequence is arithmetic.No Common Ratio Found: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. Calculate the ratios: 22 / 28, 16 / 22, 10 / 16.Sequence Classification: Perform the calculations: 22 / 28 ≈ 0.7857, 16 / 22 ≈ 0.7273, 10 / 16 = 0.625.Since the ratios between consecutive terms are not equal, the sequence does not have a common ratio and therefore is not a geometric sequence.A geometric sequence is defined by having a constant ratio between consecutive terms. Since the ratios are not constant, this sequence cannot be geometric.Based on the calculations and definitions, the sequence is arithmetic but not geometric. Therefore, the correct choice is (A) arithmetic.

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What kind of sequence is this? $\newline$ $28, 22, 16, 10, \dots$ $\newline$ 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

28, 22, 16, 10, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Differences for Arithmetic: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: $28, 22, 16, 10, \ldots$ $\newline$ Calculate the differences: $22 - 28 = -6$ , $16 - 22 = -6$ , $10 - 16 = -6$ .
Common Difference Found: Since the differences between consecutive terms are equal, we can conclude that the sequence has a common difference of $-6$ .
Check Ratios for Geometric: An arithmetic sequence is defined by having a constant difference between consecutive terms. Since we have found a common difference, this sequence is arithmetic.
No Common Ratio Found: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. Calculate the ratios: $\frac{22}{28}$ , $\frac{16}{22}$ , $\frac{10}{16}$ .
Sequence Classification: Perform the calculations: $\frac{22}{28} \approx 0.7857$ , $\frac{16}{22} \approx 0.7273$ , $\frac{10}{16} = 0.625$ .
Sequence Classification: Perform the calculations: $\frac{22}{28} \approx 0.7857$ , $\frac{16}{22} \approx 0.7273$ , $\frac{10}{16} = 0.625$ . Since the ratios between consecutive terms are not equal, the sequence does not have a common ratio and therefore is not a geometric sequence.
Sequence Classification: Perform the calculations: $\frac{22}{28} \approx 0.7857$ , $\frac{16}{22} \approx 0.7273$ , $\frac{10}{16} = 0.625$ . Since the ratios between consecutive terms are not equal, the sequence does not have a common ratio and therefore is not a geometric sequence. A geometric sequence is defined by having a constant ratio between consecutive terms. Since the ratios are not constant, this sequence cannot be geometric.
Sequence Classification: Perform the calculations: $\frac{22}{28} \approx 0.7857$ , $\frac{16}{22} \approx 0.7273$ , $\frac{10}{16} = 0.625$ . Since the ratios between consecutive terms are not equal, the sequence does not have a common ratio and therefore is not a geometric sequence. A geometric sequence is defined by having a constant ratio between consecutive terms. Since the ratios are not constant, this sequence cannot be geometric. Based on the calculations and definitions, the sequence is arithmetic but not geometric. Therefore, the correct choice is $(A)$ arithmetic.