posted by Kel on .
What is the units digit of the 100th number in this sequence: 1, 4, 8, 16, 32, 64, ...?
Correct me if I am wrong, but I believe you left out the actual 2nd number in this apparant series. It most likely reads 1-2-4-8-16-32-64-128-256-512-etc.
Note that after the first digit, the 1, the units digits follow the pattern of 2, 4, 8, 6 throughout.
Since the repeating series starts with the second number, we divide 99 by 4 = 24.75. The .75 indicates that the units digit of the 99th number of the repeating series, or the 100th number of the entire series, is the 3rd number of the repeating set of 2, 4, 8,6, or 8.
I think your first number should have been 2
anyway. ... the terms end in digits 2,4,8,6,2,4,6,8
the period is 4, 100 divides evenly by 4, so it ends in the last digit of the repeat which would be 8