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While sorting some change into piggy banks, Marco put $1$ coin in the first piggy bank, $6$ coins in the second piggy bank, $30$ coins in the third piggy bank, and $120$ coins in the fourth piggy bank. 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

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Q. While sorting some change into piggy banks, Marco put

1

coin in the first piggy bank,

6

coins in the second piggy bank,

30

coins in the third piggy bank, and

120

coins in the fourth piggy bank. What kind of sequence is this?

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

(C) both

\newline

(D) neither

Input Sequence: Marco put coins into piggy banks in the following order: $\newline$ First piggy bank: $1$ coin $\newline$ Second piggy bank: $6$ coins $\newline$ Third piggy bank: $30$ coins $\newline$ Fourth piggy bank: $120$ coins $\newline$ Let's list the number of coins in the given order. $\newline$ Sequence: $1, 6, 30, 120$
Check Differences: $1, 6, 30, 120$ $\newline$ Are the differences between consecutive terms equal? $\newline$ $6 - 1 = 5$ $\newline$ $30 - 6 = 24$ $\newline$ $120 - 30 = 90$ $\newline$ The differences are not the same, so this is not an arithmetic sequence.
Check Ratios: $1, 6, 30, 120$ $\newline$ Are the consecutive ratios of the sequence equal? $\newline$ $\frac{6}{1} = 6$ $\newline$ $\frac{30}{6} = 5$ $\newline$ $\frac{120}{30} = 4$ $\newline$ The ratios are not the same, so this is not a geometric sequence.
Sequence Analysis: The sequence has: $\newline$ no common difference. $\newline$ no common ratio. $\newline$ What type of sequence is $1, 6, 30, 120$ ? $\newline$ Since the sequence does not have a constant difference or ratio, it is neither arithmetic nor geometric.

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