anonymous
  • anonymous
Find f(5) for this sequence: f(1) = 2 and f(2) = 3, f(n) = f(1) + f(2) + f(n - 1), for n > 2. f(5) = ______ Numerical Answers Expected! Answer for Blank 1:
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
@mathstudent55
Empty
  • Empty
Plug in the values to your recurrence relation for f(1) and f(2). It will make it much easier I think!
mathstudent55
  • mathstudent55
Here is an explanation of what this means: f(1) = 2 and f(2) = 3, f(n) = f(1) + f(2) + f(n - 1), for n > 2. f(1) is the first term of the sequence. We are given f(1) = 2 f(2) is the 2nd term of the sequence, and we are told f(2) = 3 There are no calculations needed to find the first two terms. they are given.

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mathstudent55
  • mathstudent55
To calculate any term past the second term, when n > 2, then you use the given formula. f(n) = f(1) + f(2) + f(n - 1) That means that any term of the sequence (past the second term) is the sum of the first term, the second term, and the previous term.
mathstudent55
  • mathstudent55
Using the formula, let's see what we get for the 3rd term. The third term has n = 3. We need to find f(n) = f(1) + f(2) + f(n - 1) for n = 3 Let's see which terms we need to add. We replace n with 3 in the formula: f(3) = f(1) + f(2) + f(3 - 1) f(3) = f(1) + f(2) + f(2) f(3) = 2 + 3 + 3 = 8 That means the third term is 8. Now you need to do the same calculation for n = 4 and then n = 5.
anonymous
  • anonymous
oh okay
anonymous
  • anonymous
how would I do the rest i'm not too sure how to set them up
anonymous
  • anonymous
Would it be 13 for the 5th term?
anonymous
  • anonymous
@mathstudent55
mathstudent55
  • mathstudent55
Let's see. I need the 4th term first. f(4) = f(1) + f(2) + f(4 - 1) f(4) = f(1) + f(2) + f(3) = 2 + 3 + 8 = 13 f(5) = f(1) + f(2) + f(5 - 1) f(5) = f(1) + f(2) + f(4) = 2 + 3 + 13 = 18
anonymous
  • anonymous
oh okay so I said the 4th term okay. Well thank you so much!
mathstudent55
  • mathstudent55
Notice that each term is the previous term plus the first two terms. The first two terms are always 2 and 3, so you are always adding 5 to the previous term.
anonymous
  • anonymous
Alright
mathstudent55
  • mathstudent55
2 3 2 + 3 + 3 = 8 5 + 8 = 13 5 + 13 = 18 5 + 18 = 23 5 + 23 = 28 etc.
mathstudent55
  • mathstudent55
You're welcome.
anonymous
  • anonymous
oh okay I got it now. Thank you so much for explaining it to me

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