What kind of sequence is this?

Question

15, 45, 135, 405, ...

Answer 1

To identify the type of sequence for the numbers 15, 45, 135, 405, let's analyze the ratios between consecutive terms.

1. The ratio of the second term to the first term: $$\frac{45}{15}=3$$

2. The ratio of the third term to the second term: $$\frac{135}{45}=3$$

3. The ratio of the fourth term to the third term: $$\frac{405}{135}=3$$

Since each term is obtained by multiplying the previous term by 3, this sequence is a geometric sequence. The first term is 15, and the common ratio is 3.

To summarize, the sequence is a geometric sequence where:

• First term (a) = 15
• Common ratio (r) = 3

Thus, the $n$-th term of this sequence can be expressed as: $$a_n=15\times 3^{(n-1)}$$