Last year, Winchester Hardware ordered $6$ hammers in September, $30$ hammers in October, $150$ hammers in November, and $750$ hammers in December. What kind of sequence is this? $\newline$ Choices: $\newline$ (A) arithmetic $\newline$ (B) geometric $\newline$ (C) both $\newline$ (D) neither

Full solution

Q. Last year, Winchester Hardware ordered

6

hammers in September,

30

hammers in October,

150

hammers in November, and

750

hammers in December. What kind of sequence is this?

\newline

Choices:

\newline

(A) arithmetic

\newline

(B) geometric

\newline

\newline

(D) neither

Identify Pattern: Identify the pattern in the sequence of hammers ordered by Winchester Hardware. $\newline$ September: $6$ hammers $\newline$ October: $30$ hammers $\newline$ November: $150$ hammers $\newline$ December: $750$ hammers $\newline$ We need to determine if the sequence is arithmetic (where each term after the first is obtained by adding a constant), geometric (where each term after the first is obtained by multiplying the previous term by a constant), or neither.
Check Arithmetic Sequence: Check for an arithmetic sequence by finding the difference between consecutive terms. $\newline$ Difference between October and September: $30 - 6 = 24$ $\newline$ Difference between November and October: $150 - 30 = 120$ $\newline$ Difference between December and November: $750 - 150 = 600$ $\newline$ The differences are not constant, so this is not an arithmetic sequence.
Check Geometric Sequence: Check for a geometric sequence by finding the ratio between consecutive terms. $\newline$ Ratio between October and September: $\frac{30}{6} = 5$ $\newline$ Ratio between November and October: $\frac{150}{30} = 5$ $\newline$ Ratio between December and November: $\frac{750}{150} = 5$ $\newline$ The ratios are constant, so this is a geometric sequence.