Question

These are the first six terms of a sequence starting with a1 = 80:

80, 40, 20, 10, 5, 5/2, ….
Find a recursive formula for this sequence that is valid for n > 1.
Write your answer in simplest form.
an=?

Answer 1

`a _(n) = a( {r}^(n - 1) ) \\ a _(n) = 80(2 {}^(n - 1) ) \\ a _(n) = \frac{80. {2}^(n) }{ {2}^( 1) } \\a _(n) = 40( {2}^(n) ) \\ a _(n) = ( {2}^(3) * 5)( {2}^(n) ) \\ a _(n) = 5( {2}^(n + 3) )`