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On the last day of school, the first student will receive $12$ blue pens, the second student will receive $24$ blue pens, the third student will receive $48$ blue pens, and the fourth student will receive $96$ blue pens. What kind of sequence is this? $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

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Identify arithmetic and geometric sequences

Full solution

Q. On the last day of school, the first student will receive

12

blue pens, the second student will receive

24

blue pens, the third student will receive

48

blue pens, and the fourth student will receive

96

blue pens. What kind of sequence is this?

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

(C) both

\newline

(D) neither

List Blue Pen Numbers: Step $1$ : List the number of blue pens each student receives. $\newline$ First student: $12$ $\newline$ Second student: $24$ $\newline$ Third student: $48$ $\newline$ Fourth student: $96$ $\newline$ Sequence: $12, 24, 48, 96$
Check Differences: Step $2$ : Check if the differences between consecutive terms are equal. $\newline$ $24 - 12 = 12$ $\newline$ $48 - 24 = 24$ $\newline$ $96 - 48 = 48$ $\newline$ The differences are not the same.
Check Ratios: Step $3$ : Check if the ratios between consecutive terms are equal. $\newline$ $\frac{24}{12} = 2$ $\newline$ $\frac{48}{24} = 2$ $\newline$ $\frac{96}{48} = 2$ $\newline$ The ratios are the same.

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