Answer: Choice C
{1, 1, 2, 3, 5}
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We have
[tex]a_1 = 1\\a_2 = 1[/tex]
Showing the first two terms are 1,1.
The answer is between choices B and C because of this.
To get the nth term [tex]a_n[/tex], we add up the two previous terms before it [tex]a_{n-1}[/tex] and [tex]a_{n-2}[/tex]
So to get the third term [tex]a_3[/tex], we'll add up the first two terms
[tex]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[/tex]
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:
[tex]a_4 = a_2 + a_3\\\\a_4 = 1+2\\\\a_4 = 3[/tex]
Further confirming the answer. I'll let you check the next set of terms.
For more information, check out the Fibonacci numbers.
