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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
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Re: If A_n = 7n 1, what is the units digit of A33?
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31 Dec 2024, 01:02
31 Dec 2024, 01:02
1
\(A_{n} = 7^n − 1\)
To find \(A_{33}\) we will replace n with 33 in \(A_{n} = 7^n − 1\)
=> \(A_{33} = 7^{33} − 1\)
[ Watch this video to MASTER FUNCTIONS ]
To find the units' digit of \(7^{33}\), we need to find the cycle of units' digit of power of 7
\(7^1\) units’ digit is 7
\(7^2\) units’ digit is 9
\(7^3\) units’ digit is 3
\(7^4\) units’ digit is 1
\(7^5\) units’ digit is 7
=> The power repeats after every \(4^{th}\) power
=> Cycle of units' digit of power of 7 = 4
=> We need to divide the power by 4 and check the remainder
33 when divided by 4 gives 1 remainder
=> Units' digit of \(7^{33}\) = Units' digit of \(7^1\) = 7
=> Units' digit of \(7^{33} − 1\) = 7 - 1 = 6
So, Answer will be C
Hope it helps!
Watch the following video to MASTER Units Digit
To find \(A_{33}\) we will replace n with 33 in \(A_{n} = 7^n − 1\)
=> \(A_{33} = 7^{33} − 1\)
[ Watch this video to MASTER FUNCTIONS ]
To find the units' digit of \(7^{33}\), we need to find the cycle of units' digit of power of 7
\(7^1\) units’ digit is 7
\(7^2\) units’ digit is 9
\(7^3\) units’ digit is 3
\(7^4\) units’ digit is 1
\(7^5\) units’ digit is 7
=> The power repeats after every \(4^{th}\) power
=> Cycle of units' digit of power of 7 = 4
=> We need to divide the power by 4 and check the remainder
33 when divided by 4 gives 1 remainder
=> Units' digit of \(7^{33}\) = Units' digit of \(7^1\) = 7
=> Units' digit of \(7^{33} − 1\) = 7 - 1 = 6
So, Answer will be C
Hope it helps!
Watch the following video to MASTER Units Digit
