Question

Write a recursive formula for the sequence: 8, 4, 2, 1,...Tn + 1 = Tn × 12Tn + 1 = Tn × (2)Tn + 1 = Tn - 4(n - 1)Tn + 1 = Tn + 4(n - 1)

Answer 1

Given:

The sequence is:

8, 4, 2, 1,...

Required:

Find a recursive formula for the given sequence.

Explanation:

The given sequence is:

8, 4, 2, 1,...

The common ratio of the sequence is:

$\begin{gathered} \frac{4}{8}=\frac{1}{2} \\ \frac{2}{4}=\frac{1}{2} \\ \frac{1}{2} \end{gathered}$

Since the common ratio for the given series is 1/2.

$\begin{gathered} \frac{T_{n+1}}{T_n}=\frac{1}{2} \\ T_{n+1}=\frac{1}{2}T_n \end{gathered}$

Final Answer:

The recursive formula for the given sequence is

$T_{n+1}=\frac{1}{2}T_{n}$