Given:\(a_1=9^1\) and +int n,\(a_n=(10^n - 1)^n\)
Question: What is the UD (units digit) of Sn?
(1) \(n\) is even
This question is testing cyclicity.
10^+int has UD of 0 (cyclicity of 1). 9 has cyclicity of 2 (odd n gives 9, even n gives 1)
(10^2 - 1)^2 = (100 - 1)^2 = 99^2 so 9^even = 1 UD
(10^3 - 1)^3 = (1000 - 1)^3 = 999^3 so 9^odd = 9 UD
Since statement says n is even we know UD = 1, sufficient.
(2) \(n\) is prime Following the above, n could be even = 2 or odd = 3 and fulfil the constraint,
...
Question: What is the UD (units digit) of Sn?
(1) \(n\) is even
This question is testing cyclicity.
10^+int has UD of 0 (cyclicity of 1). 9 has cyclicity of 2 (odd n gives 9, even n gives 1)
(10^2 - 1)^2 = (100 - 1)^2 = 99^2 so 9^even = 1 UD
(10^3 - 1)^3 = (1000 - 1)^3 = 999^3 so 9^odd = 9 UD
Since statement says n is even we know UD = 1, sufficient.
(2) \(n\) is prime Following the above, n could be even = 2 or odd = 3 and fulfil the constraint,
...
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