andrewdangmus andrewdangmus

13-06-2018
Mathematics

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The sequence {an } is defined by a of o = 1 and a of n + 1 = 2 a of n + 2 for n = 0, 1, 2.... What is the value of a of 3?

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LammettHash LammettHash

13-06-2018

[tex]\begin{cases}a(0)=1\\a(n+1)=2a(n)+2&\text{for }n\ge0\end{cases}[/tex]

Use the second part of the definition (the recursive one):

[tex]a(1)=2a(0)+2=4[/tex]
[tex]a(2)=2a(1)+2=10[/tex]
[tex]a(3)=2a(2)+2=22[/tex]

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