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.

Step-by-step explanation:

The given sequence is:

8, 4, 2, 1,...

The common ratio of the sequence is:

`\begin{gathered} (4)/(8)=(1)/(2) \\ (2)/(4)=(1)/(2) \\ (1)/(2) \end{gathered}`

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

`\begin{gathered} (T_(n+1))/(T_n)=(1)/(2) \\ T_(n+1)=(1)/(2)T_n \end{gathered}`

Final Answer:

The recursive formula for the given sequence is

`T_(n+1)=(1)/(2)T_(n)`