Question

Define the sequence recursively using function notation. 2.5, 7.5, 22.5, 67.5, 202.5,...

Answer 1

Answer: Aₙ = Aₙ₋₁*3;  where A₀ = 2.5

Step-by-step explanation:

Let's try with some known sequences:

Arithmetic.

The difference between consecutive terms is constant:

7.5 - 2.5 = 5

22.5 - 7.5 = 15

We can already see that it is not an arithmetic sequence.

Geometric:

The ratio between consecutive terms is constant.

7.5/2.5 = 3

22.5/7.5 = 3

67.5/22.5 = 3

...

We can already see that this is a geometric sequence.

Then we can write the n-th term as:

Aₙ = Aₙ₋₁*3, where A₀ = 2.5