At a birthday party, the first child receives $658$ smiley stickers, the second child receives $658$ smiley stickers, the third child receives $658$ smiley stickers, and the fourth child receives $658$ smiley stickers. What kind of sequence is this? $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

Full solution

Q. At a birthday party, the first child receives

658

smiley stickers, the second child receives

658

smiley stickers, the third child receives

658

smiley stickers, and the fourth child receives

658

smiley stickers. What kind of sequence is this?

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Identify Problem Type: Understand the problem and identify the type of sequence. Each child is receiving the same number of smiley stickers, which is $658$ . Since the number of stickers each child receives does not change, we can determine the type of sequence by looking at the difference or ratio between the numbers.
Determine Arithmetic Sequence: Determine if the sequence is arithmetic. An arithmetic sequence is one where the difference between consecutive terms is constant. Since each child receives the same number of stickers, the difference between the number of stickers received by any two consecutive children is $0$ ( $658 - 658 = 0$ ).
Determine Geometric Sequence: Determine if the sequence is geometric. A geometric sequence is one where the ratio between consecutive terms is constant. Since each child receives the same number of stickers, the ratio between the number of stickers received by any two consecutive children is $1$ ( $658 / 658 = 1$ ).
Conclude Sequence Type: Conclude the type of sequence. $\newline$ Since the difference between consecutive terms is constant $0$ , the sequence is arithmetic. Since the ratio between consecutive terms is also constant $1$ , the sequence is also geometric. Therefore, the sequence is both arithmetic and geometric.