SOLUTION: A sequence is defined recursively by the given forumlas. Find the first 5 terms. an= (1)/(1+a(n-1) and a1=1 I am just not understanding recursive sequences.

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Question 1104290: A sequence is defined recursively by the given forumlas. Find the first 5 terms.
an= (1)/(1+a(n-1) and a1=1
I am just not understanding recursive sequences.
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  You are just given  that  a%5B1%5D = 1.


2.  Use the given formula to calculate  a%5B2%5D.

    You have  n= 2,  n-1= (2-1) = 1;  therefore, the formula takes the form

    a%5B2%5D = 1%2F%281%2Ba%5B1%5D%29 = 1%2F%281%2B1%29 = 1%2F2.    (I substituted a%5B1%5D = 1).



3.  Now, when you know a%5B2%5D, you can calculate  a%5B3%5D, using the given formula.

    You have  n= 3,  n-1= (3-1) = 2;  therefore, the formula takes the form

    a%5B3%5D = 1%2F%281%2Ba%5B2%5D%29 = 1%2F%281%2B%281%2F2%29%29 = 1%2F%282%2F2%2B1%2F2%29%29 = 1%2F%28%283%2F2%29%29 = 2%2F3.    (I substituted a%5B2%5D = 1%2F2).



4.  Now, when you know a%5B3%5D, you can calculate  a%5B4%5D, using the given formula.

    You have  n= 4,  n-1= (4-1) = 3;  . . . and you can continue from this point on your own,  using the same logic . . .


It is how the recursive formulas work: if you know all preceding terms, you can calculate the next term, using the given recursive formula.


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If you still have questions or need more explanation, let me know by posting your message through the "Thank you" window.

If you do, do not forget to refer to the problem's ID number, which is 1104290.

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