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Tyrone has a garden and likes to put flowers from his garden into pretty vases. Tyrone put $11$ flowers in the first vase, $22$ flowers in the second vase, $44$ flowers in the third vase, and $88$ flowers in the fourth vase. 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. Tyrone has a garden and likes to put flowers from his garden into pretty vases. Tyrone put

11

flowers in the first vase,

22

flowers in the second vase,

44

flowers in the third vase, and

88

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

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

(C) both

\newline

(D) neither

Arrange flowers in vases: Tyrone put flowers into vases in the following order: $\newline$ First vase: $11$ flowers $\newline$ Second vase: $22$ flowers $\newline$ Third vase: $44$ flowers $\newline$ Fourth vase: $88$ flowers $\newline$ List the number of flowers in the given order to identify the sequence. $\newline$ Sequence: $11, 22, 44, 88$
Identify sequence: $11, 22, 44, 88$ $\newline$ Check if the differences between consecutive terms are equal to determine if it's an arithmetic sequence. $\newline$ $22 - 11 = 11$ $\newline$ $44 - 22 = 22$ $\newline$ $88 - 44 = 44$ $\newline$ The differences between each consecutive term are not the same, so it is not an arithmetic sequence.
Check arithmetic sequence: $11, 22, 44, 88$ $\newline$ Check if the ratios of consecutive terms are equal to determine if it's a geometric sequence. $\newline$ $\frac{22}{11} = 2$ $\newline$ $\frac{44}{22} = 2$ $\newline$ $\frac{88}{44} = 2$ $\newline$ The ratio between each consecutive term is the same, so it is a geometric sequence.

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