Question

7) Given that Sn=3-2^(-4n)

is the sum of the first n terms of a sequence.
Un is the n term.
a) Express Un+1 in terms of n.
b) Deduce that the
sequence is a geometric progression.
​

Answer 1

Explanation:

`s_(n)=3-2^(-4n)\\s_(n+1)=3-2^(-4(n+1))=3-2^(-4n) *2^(-4)\\s_(n+1)-s_(n)=3-2^(-4n)*2^-4-3+2^(-4n)`

`=2^(-4n)-2^(-4n)*2^(-4)\\=2^(-4n)(1-2^(-4))\\=2^(-4n)((2^4-1)/(2^4))\\=2^(-4n)(15)/(16)\\U_(n+1)=15*2^(-4(n+1))`