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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
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GPA: 3.39
If A_n = 7n − 1, what is the units digit of A33?
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09 Feb 2021, 09:39
09 Feb 2021, 09:39
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If \(A_{n} = 7^n − 1\), what is the units digit of \(A_{33}\)?
A. 1
B. 3
C. 6
D. 7
E. 9
A. 1
B. 3
C. 6
D. 7
E. 9
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If A_n = 7n − 1, what is the units digit of A33?
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09 Feb 2021, 22:23
09 Feb 2021, 22:23
1
GeminiHeat wrote:
If \(A_{n} = 7^n − 1\), what is the units digit of \(A_{33}\)?
A. 1
B. 3
C. 6
D. 7
E. 9
A. 1
B. 3
C. 6
D. 7
E. 9
\(A_{33}\) = \(7^{33}\) - 1
7 has a repeating pattern of 4 (1, 9, 3, and 1) i.e. the units digit repeats itself every 4 powers of 7
\(7^1\) = 7
\(7^2\) = 49
\(7^3\) = 343
\(7^4\) = 2401
\(7^5\) = 16807
Now, to find the units digit in \(7^{33}\), we will divide 33 with 4 and find the remainder.
Here the remainder is 1, so the first digit in the repeating pattern would be the units digit of \(7^{33}\), which is 7
So, \(A_{33}\) = \(7^{33}\) - 1 = ____7 - 1 = ____6
Hence, option C
gmatclubot
If A_n = 7n − 1, what is the units digit of A33? [#permalink]
09 Feb 2021, 22:23
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