High School

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For a sequence defined by [tex]f(1) = 13[/tex] and [tex]f(n) = 2f(n-1) + (n-2)[/tex], which of the following is the value of [tex]f(4)[/tex]?

1. 53
2. 76
3. 108
4. 126

Answer :

Given that:
f(1)=13 and 2f(n-1)+(n-2)
then:
f(4) will be found as follows:
f(2)=2f(2-1)=2f(1)=2*13=26
f(3)=2f(3-1)+(3-2)=2f(2)+1=2*26+1=53
f(4)=2f(4-1)+(4-2)=2f(3)+(4-2)=2(53)+2=108

Thus:
Answer:(3) 108

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