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08 Jun 2023, 03:00
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
82% (02:11) correct
18%
(02:19)
wrong
based on 147
sessions
History
Date
Time
Result
Not Attempted Yet
\(x_1 = 1\), for all positive integers, \(x_n = 1+7x_{n-1}\) , what is the units digit of \(x_{102}\)?
A. 3
B. 5
C. 8
D. 11
E. 15
A. 3
B. 5
C. 8
D. 11
E. 15
13 Jun 2023, 10:58
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Bunuel
Given sequence: \(x_n = 1+7x_{n-1}\)
\(x_1 =1 \)
\(x_2 = 1+7(1) = 8\)
\(x_3 = 1+7(8) = 57\)
\(x_4 =1+7(57) = 400\)
\(x_5 =1+7(400)= 2801\)
\(x_6 = 1+7(2801) =....8\)
Thus we see that the unit digit of the given sequence has a cyclicity of \(4\) i.e. the unit digit repeats after every \(4\) terms.
Therefore \(x_{102} = 4*25 +2 \)
Thus the unit digit will be the same as \(x_2 \), which is \(8\)
Ans C
Hope it helps.
Bunuel small typo in the question. Thank you.
19 May 2025, 21:20
Kudos
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