Question

Find the first four terms of the recursive sequence defined by the following formula:

an =
an-1
4
where a4 = 2
1
4


,
,
, 2
1
4

Answer 1

The recurrence is a_n = (1/4) a_{n-1}, and a_4 = 2 1/4 = 9/4. Work backward by multiplying by 4:

- a_3 = 4·a_4 = 4·(9/4) = 9
- a_2 = 4·a_3 = 4·9 = 36
- a_1 = 4·a_2 = 4·36 = 144

So the first four terms are 144, 36, 9, 2 1/4.