SOLUTION: Write the first four terms of the recursive sequence. A_1=-5,a_n=n+a

SOLUTION: Write the first four terms of the recursive sequence. A_1=-5,a_n=n+a_n-1for n>2

Question 1122871: Write the first four terms of the recursive sequence.

A_1=-5,a_n=n+a_n-1for n>2

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

This is simple if you understand what a recursive definition of a sequence is.

By the way, the given definition is faulty; it tells us what a(1) is, and it tells us how to find a(n) for n greater than 2. But it doesn't tell us how to find a(2).

So the correct recursive definition would show

a(1) = -5; a(n) = n+a(n-1) for n > 1 (not for n > 2)

So the recursive definition first defines the 1st term: a(1) = -5.

Then it tells you how to find each successive term ("a(n)") from the preceding term ("a(n-1)"). Specifically, it says that, for n > 1 the value of the next term is the current value of n ("n"), plus the value of the preceding term ("a(n-1)").

So the value of a(2) is 2, plus a(1), or 2+(-5) = -3.

Then similarly the value of a(3) is 3, plus a(2), or 3+-3 = 0.

The problem only asks you for the first 4 terms, and I have found 3 of them for you. It should be easy to find one more term in the sequence.

However, if these recursive sequences are something new to you, I would recommend finding at least 3 or 4 more terms in the sequence, to give you a better feel for how recursive definitions work.
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