Trisha's Pizzeria made $9$ pizzas on Monday, $16$ pizzas on Tuesday, $25$ pizzas on Wednesday, and $36$ pizzas on Thursday. What kind of sequence is this? $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

View step-by-step help

Home

Math Problems

Grade 8

Identify arithmetic and geometric sequences

Full solution

Q. Trisha's Pizzeria made

9

pizzas on Monday,

16

pizzas on Tuesday,

25

pizzas on Wednesday, and

36

pizzas on Thursday. What kind of sequence is this?

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Identify Pattern of Pizzas: Let's list the number of pizzas made each day to see if we can identify a pattern: $\newline$ Monday: $9$ pizzas $\newline$ Tuesday: $16$ pizzas $\newline$ Wednesday: $25$ pizzas $\newline$ Thursday: $36$ pizzas
Check for Arithmetic Sequence: To determine if this is an arithmetic sequence, we need to check if the difference between consecutive terms is constant. $\newline$ Difference between Tuesday and Monday: $16 - 9 = 7$ $\newline$ Difference between Wednesday and Tuesday: $25 - 16 = 9$ $\newline$ Difference between Thursday and Wednesday: $36 - 25 = 11$ $\newline$ Since the differences are not constant, this is not an arithmetic sequence.
Check for Geometric Sequence: To determine if this is a geometric sequence, we need to check if the ratio between consecutive terms is constant. $\newline$ Ratio of Tuesday to Monday: $\frac{16}{9}$ (not a whole number) $\newline$ Ratio of Wednesday to Tuesday: $\frac{25}{16}$ (not a whole number) $\newline$ Ratio of Thursday to Wednesday: $\frac{36}{25}$ (not a whole number) $\newline$ Since the ratios are not constant, this is not a geometric sequence.
Pattern of Perfect Squares: Let's look for another pattern. We notice that the number of pizzas made each day are perfect squares. $\newline$ Monday: $9$ ( $3^2$ ) $\newline$ Tuesday: $16$ ( $4^2$ ) $\newline$ Wednesday: $25$ ( $5^2$ ) $\newline$ Thursday: $36$ ( $6^2$ ) $\newline$ The sequence of pizzas made each day corresponds to the sequence of perfect squares.
Conclusion: Since the sequence is neither arithmetic nor geometric, and it follows the pattern of perfect squares, the correct choice is: $\newline$ (D) neither