What kind of sequence is this? 378, 359, 343, 330, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Arithmetic Sequence: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: 378, 359, 343, 330, ... Difference between first and second term: 359 - 378 = -19 Difference between second and third term: 343 - 359 = -16 Difference between third and fourth term: 330 - 343 = -13Check Geometric Sequence: The differences between consecutive terms are not constant. The differences are decreasing by 3 each time (-19, -16, -13). This means the sequence is not arithmetic.Sequence is Neither Arithmetic nor Geometric: Now let's check if the sequence is geometric by finding the ratios between consecutive terms. Ratio of second to first term: 359 / 378 ≈ 0.9497 Ratio of third to second term: 343 / 359 ≈ 0.9554 Ratio of fourth to third term: 330 / 343 ≈ 0.9621The ratios between consecutive terms are not constant. This means the sequence is not geometric.Since the sequence is neither arithmetic (no common difference) nor geometric (no common ratio), the correct choice is (D) neither.

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What kind of sequence is this? $\newline$ $378, 359, 343, 330, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Algebra 2

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Q. What kind of sequence is this?

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378, 359, 343, 330, \dots

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Choices:

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(A) arithmetic

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(B) geometric

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\newline

(D) neither

Check Arithmetic Sequence: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. $\newline$ Given sequence: $378, 359, 343, 330, \dots$ $\newline$ Difference between first and second term: $359 - 378 = -19$ $\newline$ Difference between second and third term: $343 - 359 = -16$ $\newline$ Difference between third and fourth term: $330 - 343 = -13$
Check Geometric Sequence: The differences between consecutive terms are not constant. The differences are decreasing by $3$ each time ( $-19$ , $-16$ , $-13$ ). This means the sequence is not arithmetic.
Sequence is Neither Arithmetic nor Geometric: Now let's check if the sequence is geometric by finding the ratios between consecutive terms. $\newline$ Ratio of second to first term: $\frac{359}{378} \approx 0.9497$ $\newline$ Ratio of third to second term: $\frac{343}{359} \approx 0.9554$ $\newline$ Ratio of fourth to third term: $\frac{330}{343} \approx 0.9621$
Sequence is Neither Arithmetic nor Geometric: Now let's check if the sequence is geometric by finding the ratios between consecutive terms. $\newline$ Ratio of second to first term: $\frac{359}{378} \approx 0.9497$ $\newline$ Ratio of third to second term: $\frac{343}{359} \approx 0.9554$ $\newline$ Ratio of fourth to third term: $\frac{330}{343} \approx 0.9621$ The ratios between consecutive terms are not constant. This means the sequence is not geometric.
Sequence is Neither Arithmetic nor Geometric: Now let's check if the sequence is geometric by finding the ratios between consecutive terms. $\newline$ Ratio of second to first term: $\frac{359}{378} \approx 0.9497$ $\newline$ Ratio of third to second term: $\frac{343}{359} \approx 0.9554$ $\newline$ Ratio of fourth to third term: $\frac{330}{343} \approx 0.9621$ The ratios between consecutive terms are not constant. This means the sequence is not geometric.Since the sequence is neither arithmetic (no common difference) nor geometric (no common ratio), the correct choice is $(D)$ neither.