Mathematics, 08.06.2020 06:57 maystrenko53

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.

Answers

Step-by-step explanation:

$s_{n}=3-2^{-4n}\\s_{n+1}=3-2^{-4(n+1)}=3-2^{-4n} *2^{-4}\\s_{n+1}-s_{n}=3-2^{-4n}*2^-4-3+2^{-4n}$

$=2^{-4n}-2^{-4n}*2^{-4}\\=2^{-4n}(1-2^{-4})\\=2^{-4n}(\frac{2^4-1}{2^4})\\=2^{-4n}\frac{15}{16}\\U_{n+1}=15*2^{-4(n+1)}$

Answer from: Quest

what? that isnt a question

step-by-step explanation:

The top of the arrow you can't see but it's the j

Answer from: Quest

Looks pretty good to me!

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7) Given that Sn=3-2^(-4n) is the sum of the first n terms of a sequence.
Un is the n term.