Question 1182732: Start with the number 1 and create the sequence:
1,2,4,8,16,22,24,28
where each number is the sum of the previous number and its final digit. How many numbers in the sequence are less than 1000?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Write out the next 10-20 numbers in the sequence....
1, 2, 4, 8, 16, 22, 24, 28, 36, 42, 44, 48, 56, 62, 64, 68, 76, 82, 84, 88, 96, ...
... and look for a pattern:
1, 2, 4, 8, 16 // 22, 24, 28, 36 // 42, 44, 48, 56 // 62, 64, 68, 76 // 82, 84, 88, 96 // ...
5 numbers less than 19
4 more numbers 20 to 39
4 more number 40 to 59
4 more numbers 60 to 79
4 more numbers 80 to 99
...
It should be clear that the pattern will continue.
There are 4 numbers in the sequence in every interval of 20 consecutive integers, except there is 1 additional number in the sequence among the first 20 integers.
The number of intervals of length 20 up to 1000 is 1000/20 = 50; so
ANSWER: the number of numbers in the sequence less than 1000 is 50(4)+1 = 201.
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