Question

identify the sequence below as arithmetic, geometric, or neither. then find the next two terms.
15, 18, 21, 24, ...
choose the correct type of sequence below.
○ neither
○ geometric
○ arithmetic

Explanation:

Step1: Check for arithmetic sequence

To check if it's arithmetic, find the difference between consecutive terms.
$18 - 15 = 3$, $21 - 18 = 3$, $24 - 21 = 3$. The common difference is 3, so it could be arithmetic.

Step2: Check for geometric sequence

To check if it's geometric, find the ratio between consecutive terms.
$\frac{18}{15} = 1.2$, $\frac{21}{18} \approx 1.1667$, $\frac{24}{21} \approx 1.1429$. Ratios are not equal, so not geometric.

Step3: Find next two terms

Since it's arithmetic with common difference 3, next term after 24 is $24 + 3 = 27$, then $27 + 3 = 30$.

Answer:

The sequence is arithmetic. The next two terms are 27 and 30. The correct option for the type of sequence is: arithmetic.