Question

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

Answer 1

It looks like the recursive sequence is

$a_n = \dfrac{a_{n-1}}2$

By substitution, we have

$a_{n-1} =\dfrac{a_{n-2}}2 \implies a_n = \dfrac{a_{n-2}}{2^2}$

$a_{n-2} = \dfrac{a_{n-3}}2 \implies a_n = \dfrac{a_{n-3}}{2^3}$

$a_{n-3} = \dfrac{a_{n-4}}2 \implies a_n = \dfrac{a_{n-4}}{2^4}$

and so on, down to

$a_n = \dfrac{a_1}{2^{n-1}}}$

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

$a_7 = \dfrac{64}{2^{7-1}} = \dfrac{64}{2^6} = \dfrac{64}{64} = \boxed{1}$