Question

HELP !!!!

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

Answer 1

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.