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Unit digit of a series.

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Unit digit of a series. [#permalink] New post 31 Jul 2010, 13:50
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S(n)= 4^n +5^(n+1) +3 what is the unit digit of s(100)
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Re: Unit digit of a series. [#permalink] New post 31 Jul 2010, 14:04
Expert's post
S(n)= 4^n +5^(n+1) +3

The way to solve this would be to look at each individual term.
4^1 = 4
4^2 = 16
4^3 = 64
and so on. So, the cyclicity of this is 2. Every 2 terms the last digit is 4 when the n is odd and 6 when n is even.

With 5, its always 5.

If n = 100, it's an even number and hence 4^100 will end in 6 and 5^101 will end in 5.

Hence the sum of last digits will be 6+5+3 = 14 so it'd be 4.
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Re: Unit digit of a series. [#permalink] New post 02 Aug 2010, 06:22
If n = 100, it's an even number and hence 4^100 will end in 6 and 5^101 will end in 5.

6+5+3
; so it'd be 4.
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Re: Unit digit of a series.   [#permalink] 02 Aug 2010, 06:22
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Unit digit of a series.

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