Question

part 1 of 3
a new optical illusion is posted on the internet. write a recursive formula to describe the pattern. then, write the explicit formula that can be
used to find the number of times the optical illusion is shared after eight hours.

a₁ =
ₙ =
(simplify your answers. )

Explanation:

Step1: Identify the first term

From the table, at Hour 1, the number of shares \(a_1 = 20\).

Step2: Determine the common ratio

To find the common ratio \(r\), divide the second term by the first term: \(\frac{80}{20}=4\), and check with the third term: \(\frac{320}{80}=4\). So the common ratio \(r = 4\).
For a geometric sequence, the recursive formula is \(a_n=a_{n - 1}\times r\) with \(a_1\) as the first term. So \(a_1 = 20\) and \(a_n=a_{n - 1}\times4\) for \(n\geq2\).

Answer:

\(a_1=\boldsymbol{20}\)
\(a_n=\boldsymbol{4a_{n - 1}}\) (for \(n\geq2\))