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HELP !!!!

What are the first five terms in the recursive
sequence defined by the following?
a1=1
a2
=1
On
= An-2 + On-1

HELP !!!! What are the first five terms in the recursive sequence defined by the following-example-1

1 Answer

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Answer: Choice C

{1, 1, 2, 3, 5}

===============================================

We have


a_1 = 1\\a_2 = 1

Showing the first two terms are 1,1.

The answer is between choices B and C because of this.

To get the nth term
a_n, we add up the two previous terms before it
a_(n-1) and
a_(n-2)

So to get the third term
a_3, we'll add up the first two terms


a_n = a_(n-2) + a_(n-1)\\\\a_3 = a_(3-2) + a_(3-1)\\\\a_3 = a_1 + a_2\\\\a_3 = 1 + 1\\\\a_3 = 2

The third term is therefore 2.

The sequence so far is {1,1,2} which matches with the first three terms of choice C.

Then we can say:


a_4 = a_2 + a_3\\\\a_4 = 1+2\\\\a_4 = 3

Further confirming the answer. I'll let you check the next set of terms.

For more information, check out the Fibonacci numbers.

User Crono
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