If F(n) = F(n-1) + (n-1)
F(5) = 11
What is F(1)?
Math help needed.
Use the recursion relation that they gave you, backwards.
F(n-1) = F(n)-(n-1)
Let n = 5 for starters
F(4) = F(5) -4 = 7
Now let n = 4
F(3) = F(4) -3 = 4
Coininuing in this manner,
F(2) = F(3) -2 = 2
F(1) = F(2) -1 = 1
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To find the value of F(1) using the given equation F(n) = F(n-1) + (n-1), we can work backward from F(5) = 11.
Starting with F(5) = 11, we can substitute n = 4 into the equation:
F(4) = F(4-1) + (4-1)
F(4) = F(3) + 3
Now, let's continue substituting the values until we reach F(1):
F(3) = F(3-1) + (3-1)
F(3) = F(2) + 2
F(2) = F(2-1) + (2-1)
F(2) = F(1) + 1
Finally, substituting F(2) back into the equation F(2) = F(1) + 1:
F(1) + 1 = 11
F(1) = 11 - 1
F(1) = 10
Therefore, F(1) equals 10.