Problem

Identify the Fibonacci sequence. (A) $1,2,3,4,5,6,7, \ldots$ (B) $2,4,6,8,9,10,12 \ldots$ (C) $1,1,2,3,5,8,13, \ldots$ (D) $3,6,9,12,15,18, \ldots$

Solution

Step 1 :The Fibonacci sequence is defined as a sequence where each term is the sum of the previous two terms.

Step 2 :Let's check each option:

Step 3 :(A) \(1,2,3,4,5,6,7, \ldots\) This sequence is not a Fibonacci sequence because each term is not the sum of the previous two terms. For example, \(2+3=5\) but the next term is \(4\).

Step 4 :(B) \(2,4,6,8,9,10,12 \ldots\) This sequence is not a Fibonacci sequence because each term is not the sum of the previous two terms. For example, \(4+6=10\) but the next term is \(8\).

Step 5 :(C) \(1,1,2,3,5,8,13, \ldots\) This sequence is a Fibonacci sequence because each term is the sum of the previous two terms. For example, \(1+1=2\), \(1+2=3\), \(2+3=5\), \(3+5=8\), and \(5+8=13\).

Step 6 :(D) \(3,6,9,12,15,18, \ldots\) This sequence is not a Fibonacci sequence because each term is not the sum of the previous two terms. For example, \(3+6=9\) but the next term is \(12\).

Step 7 :So, the Fibonacci sequence is (C) \(1,1,2,3,5,8,13, \ldots\).

Step 8 :\(\boxed{\text{The Fibonacci sequence is (C) } 1,1,2,3,5,8,13, \ldots\)}

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