Question 1133036: In the sequence 1,4,5,6,7,8,10,16,18,... each number after the first two is the next number that can be expressed as the sum of two previous numbers in only one way. For example, 10 is included because 6+4 = 10, and there is no other sum of two numbers in the sequence that equals 10. The number 15 is not included because both 10+5 and 8+7 equals 15. In a similar sequence that begins with the two numbers 100 and 101, the sum of the first ten terms is...
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website! Previously answered (Question 1132971)
The solution is copied here.
E) 3415
But you gain nothing from the problem if we show you the solution. You need to get the exercise in logical reasoning that is required to solve the problem.
I'll get you started.
The first two numbers are given: 100 and 101.
The only number that can be next (third) is the sum of the first two: 201. The sequence is now 100, 101, 201.
Adding 100 and 201 gives 301; adding 101 and 201 gives 302; and there are no other ways to get either of those sums. So the 4th and 5th numbers are 301 and 302. The sequence is now 100, 101, 201, 301, 302.
At this point, to help you when you do the work to finish the problem, notice that for the first several numbers in the sequence (probably far more than the 10 we are looking for), the middle digit will be 0, and the hundreds digit will be larger than the units digit.
To continue, then....
The next number we can make is 401; and we can make it in only one way: 100+301. The sequence is now 100, 101, 201, 301, 302, 401.
The next number we can make is 402. However, we can make it in two different ways: 100+302 or 101+301. So the next number in the sequence is NOT 402.
I'll stop there, except to give you some things to think about.
The next number you will look at is 403. After that you will look at 501, 502, 503, and 504. Then you might not yet have the first 10 terms of the sequence, so you might need to look at 601, 602, ....
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