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
To find the units digit of the 100th number in the sequence 1, 4, 8, 16, 32, 64, we can observe a pattern:
- The units digit of 1 is 1.
- The units digit of 4 is 4.
- The units digit of 8 is 8.
- The units digit of 16 is 6.
- The units digit of 32 is 2.
- The units digit of 64 is 4.
From the above pattern, we can see that the units digit repeats every 4 numbers. Since the sequence continues, we can determine that the units digit of the 100th number will be the same as the units digit of the 96th number, which is 2.
Therefore, the units digit of the 100th number in the sequence is 2.
To determine the units digit of the 100th number in the given sequence, we can start by observing the pattern in the units digits of the sequence.
The units digits of the sequence are: 1, 4, 8, 6, 2, 4, 8, 6, 2, ...
We can notice that the units digits repeat in a cycle of four: 1, 4, 8, 6. After the number 6, the units digit goes back to 2 and the cycle continues.
Since the cycle has a length of four, we can divide 100 by 4 to find out how many complete cycles are in the sequence: 100 / 4 = 25.
This means that there are 25 complete cycles of the units digits in the sequence. Therefore, the units digit of the 100th number will be the same as the units digit of the 25th number in the sequence.
The 25th number in the sequence can be found by multiplying 24 by 4 (the length of the cycle) and adding 1: 24 * 4 + 1 = 97.
Therefore, the units digit of the 100th number in the sequence is the same as the units digit of the 97th number, which is 7.