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Colette is planting flowers in her garden. She plants $14$ flowers in the first row, $28$ flowers in the second row, $56$ flowers in the third row, and $112$ flowers in the fourth row. 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. Colette is planting flowers in her garden. She plants

14

flowers in the first row,

28

flowers in the second row,

56

flowers in the third row, and

112

flowers in the fourth row. What kind of sequence is this?

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

(C) both

\newline

(D) neither

Identify pattern in sequence: Step $1$ : Identify the pattern in the sequence of flowers planted in each row. $\newline$ First row: $14$ flowers, Second row: $28$ flowers, Third row: $56$ flowers, Fourth row: $112$ flowers. $\newline$ To find the pattern, check the ratio of consecutive terms. $\newline$ $28 \div 14 = 2$ , $56 \div 28 = 2$ , $112 \div 56 = 2$ . $\newline$ Each term is multiplied by $2$ to get the next term.
Determine sequence type: Step $2$ : Determine the type of sequence based on the pattern found in Step $1$ . $\newline$ Since each term is obtained by multiplying the previous term by a constant $2$ , the sequence is a geometric sequence.

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