What kind of sequence is this? 7, 21, 84, 420, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Arithmetic Differences: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: 7, 21, 84, 420, ... Calculate the differences: 21 - 7 = 14, 84 - 21 = 63, 420 - 84 = 336.Verify Equality of Differences: Now, let's see if these differences are equal. Are the consecutive differences in the sequence equal? 14, 63, and 336 are not equal. This means the sequence is not arithmetic.Check Geometric Ratios: Next, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: 7, 21, 84, 420, ... Calculate the ratios: 21 / 7 = 3, 84 / 21 = 4, 420 / 84 = 5.Verify Equality of Ratios: Now, let's see if these ratios are equal. Are the ratios between consecutive terms in the sequence equal? 3, 4, and 5 are not equal. This means the sequence is not geometric.Identify Sequence Type: 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? $\newline$ $7, 21, 84, 420, \dots$ $\newline$ 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?

\newline

7, 21, 84, 420, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Arithmetic Differences: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: $7, 21, 84, 420, \ldots$ $\newline$ Calculate the differences: $21 - 7 = 14$ , $84 - 21 = 63$ , $420 - 84 = 336$ .
Verify Equality of Differences: Now, let's see if these differences are equal. Are the consecutive differences in the sequence equal? $14$ , $63$ , and $336$ are not equal. $\newline$ This means the sequence is not arithmetic.
Check Geometric Ratios: Next, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: $7, 21, 84, 420, \ldots$ $\newline$ Calculate the ratios: $\frac{21}{7} = 3$ , $\frac{84}{21} = 4$ , $\frac{420}{84} = 5$ .
Verify Equality of Ratios: Now, let's see if these ratios are equal. Are the ratios between consecutive terms in the sequence equal? $3$ , $4$ , and $5$ are not equal. $\newline$ This means the sequence is not geometric.
Identify Sequence Type: Since the sequence is neither arithmetic (no common difference) nor geometric (no common ratio), the correct choice is $(D)$ neither.