Several terms of a sequence $\{a_n{\}}_n=1^{}$ are given.

a$.$ Find the next two terms of the sequence.

b$.$ Find a recurrence relation that generates the sequence $($supply the initial value of the index and the first term of the sequence$).$

c$.$ Find an explicit formula for the nth term of the sequence.

$\{1,2,4,8,16,$dots$\}$

a$.$ The next two terms of the sequence are $a_6=32$ and $a_7=64.($Simplify your answers.$)$

b$.$ A recurrence relation that generates the sequence is $a_{n1}=2a_n,a_1=1,$ for $n1.$

c$.$ An explicit formula for the general nth term of the sequence is $a_n=,n1.$