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The tens digit of 6^17 is
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11 Jul 2021, 03:55
2
GeminiHeat wrote:
The tens digit of 6^17 is
A. 1
B. 3
C. 5
D. 7
E. 9
62=36 63=216 64=1296 65=7776 66=56656 67=279936
We have a pattern of: 3, 1, 9, 7, 5 i.e. the digits would repeat every 5 terms
3 as ten's digit: 62,67,612,617,.... 1 as ten's digit: 63,68,613,618,.... 9 as ten's digit: 64,69,614,619,.... 7 as ten's digit: 65,610,615,620,.... 5 as ten's digit: 66,611,616,621,....
The tens digit of 6^17 is
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13 Sep 2024, 20:51
1
We need to find the tens digit of 6^17
Last Two digits of 6 follow following pattern
Last Two Digits of 6^1 = 06 Last Two Digits of 6^2 = 36 Last Two Digits of 6^3 = 36*6 = 16 Last Two Digits of 6^4 = 16*6 = 96 Last Two Digits of 6^5 = 96*6 = 76 Last Two Digits of 6^6 = 76*6 = 56 Last Two Digits of 6^7 = 56*6 = 36 [ same as 6^2 ] Last Two Digits of 6^8 = 36*6 = 16 [ same as 6^3 ]
=> So, from 6^2 cycle of tens' digit repeats as 3, 1, 9, 7 , 5, 3, 1 9, 7 , 5 => We have a cycle of 5 from the 2nd term => Tens' digit of 6^17 = Now 17 = 1(6^1 not part of cycle) + 15 (cycle of 5*3) + 1 (as cycle starts from 2nd term) = First term of the cycle = 3