Sweet Time Bakery just opened and is increasing the number of items they bake. For example, the bakery made $7$ carrot cakes in December, $20$ carrot cakes in January, $33$ carrot cakes in February, and $46$ carrot cakes in March. What kind of sequence is this? $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

Full solution

Q. Sweet Time Bakery just opened and is increasing the number of items they bake. For example, the bakery made

7

carrot cakes in December,

20

carrot cakes in January,

33

carrot cakes in February, and

46

carrot cakes in March. What kind of sequence is this?

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Identify Sequence Type: To determine the type of sequence, we need to look at the differences or ratios between the terms.
Calculate Differences: First, let's find the differences between the consecutive terms: $\newline$ January - December: $20 - 7 = 13$ $\newline$ February - January: $33 - 20 = 13$ $\newline$ March - February: $46 - 33 = 13$
Confirm Arithmetic Sequence: Since the differences between the consecutive terms are constant, this indicates that the sequence is an arithmetic sequence.
Check Given Choices: Now, let's check the choices given: $\newline$ (A) arithmetic - This is the correct choice because the differences between the terms are constant. $\newline$ (B) geometric - This would be the case if the ratio between the terms was constant, which it is not. $\newline$ (C) both - A sequence cannot be both arithmetic and geometric unless it is a constant sequence, which this is not. $\newline$ (D) neither - This is not correct because we have already established that the sequence is arithmetic.