At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Plug in the values to your recurrence relation for f(1) and f(2). It will make it much easier I think!
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.
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.
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.
how would I do the rest i'm not too sure how to set them up
Would it be 13 for the 5th term?
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
oh okay so I said the 4th term okay. Well thank you so much!
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.
2 3 2 + 3 + 3 = 8 5 + 8 = 13 5 + 13 = 18 5 + 18 = 23 5 + 23 = 28 etc.
oh okay I got it now. Thank you so much for explaining it to me