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Sequence - Finding a Pattern

For COMPETITION
Number of Total Problems: 1.
FOR PRINT ::: (Book)

Problem Num : 1

From : AMC10B

Type:

Section:Sequence

Theme:
Adjustment# : 0

Difficulty: 1

'
The Fibonacci sequence $1,1,2,3,5,8,13,21,ldots$ starts with two 1s, and each term afterwards is the sum of its two predecessors. Which one of the ten digits is the last to appear in the units position of a number in the Fibonacci sequence?
$mathrm{(A) 0 } qquad mathrm{(B) 4 } qquad mathrm{(C) 6 } qquad mathrm{(D) 7 } qquad mathrm{(E) 9 }$
'

Category Finding a Pattern

Analysis

Solution/Answer
Note that any digits other than the units digit will not affect the answer. So to make computation quicker, we can just look at the Fibonacci sequence in $mod{10}$ :
$1,1,2,3,5,8,3,1,4,5,9,4,3,7,0,7,7,4,1,5,6,....$
The last digit to appear in the units position of a number in the Fibonacci sequence is $6 Longrightarrow oxed{mathrm{C}}$ .

Answer:

Array ( [0] => 8212 ) 1