What kind of sequence is this? 12, 48, 192, 768, ... Choices: (A)arithmetic (B)geometric (C)both (D)neither

Check Differences: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: 12, 48, 192, 768, ... Difference between the first and second term: 48 - 12 = 36 Difference between the second and third term: 192 - 48 = 144 Difference between the third and fourth term: 768 - 192 = 576 Are these differences equal? 36 ≠ 144 ≠ 576Check Ratios: Since the differences are not equal, the sequence is not arithmetic. Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: 12, 48, 192, 768, ... Ratio of the second to the first term: 48 / 12 = 4 Ratio of the third to the second term: 192 / 48 = 4 Ratio of the fourth to the third term: 768 / 192 = 4 Are these ratios equal? Yes, all ratios are equal to 4.Identify Sequence Type: Since the sequence has a common ratio and not a common difference, it is a geometric sequence.

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What kind of sequence is this? $\newline$ $12, 48, 192, 768, \dots$ $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Q. What kind of sequence is this?

\newline

12, 48, 192, 768, \dots

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Check Differences: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. $\newline$ Given sequence: $12, 48, 192, 768, \dots$ $\newline$ Difference between the first and second term: $48 - 12 = 36$ $\newline$ Difference between the second and third term: $192 - 48 = 144$ $\newline$ Difference between the third and fourth term: $768 - 192 = 576$ $\newline$ Are these differences equal? $\newline$ $36 \neq 144 \neq 576$
Check Ratios: Since the differences are not equal, the sequence is not arithmetic. Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. $\newline$ Given sequence: $12, 48, 192, 768, \ldots$ $\newline$ Ratio of the second to the first term: $\frac{48}{12} = 4$ $\newline$ Ratio of the third to the second term: $\frac{192}{48} = 4$ $\newline$ Ratio of the fourth to the third term: $\frac{768}{192} = 4$ $\newline$ Are these ratios equal? $\newline$ Yes, all ratios are equal to $4$ .
Identify Sequence Type: Since the sequence has a common ratio and not a common difference, it is a geometric sequence.