Question

Help pleaseeeee find the 7th term in the sequence with the following definition:

a_1=64
a_n=a_n-1/2

Answer 1

It looks like the recursive sequence is

`a_n = \frac{a_(n-1)}2`

By substitution, we have

`a_(n-1) =\frac{a_(n-2)}2 \implies a_n = (a_(n-2))/(2^2)`

`a_(n-2) = \frac{a_(n-3)}2 \implies a_n = (a_(n-3))/(2^3)`

`a_(n-3) = \frac{a_(n-4)}2 \implies a_n = (a_(n-4))/(2^4)`

and so on, down to

`a_n = (a_1)/(2^(n-1))}`

Given that
`a_1=64`, it follows that the 7th term in the sequence is

`a_7 = (64)/(2^(7-1)) = (64)/(2^6) = (64)/(64) = \boxed{1}`