Find numbers/sum in sequence

Question

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 equal 15. In a similar sequence that begins with the two numbers 100 and 101, the sum of the first ten terms is 

I have no clue how to do this, please help

Answer 1

The sequence begins with 100, 101.

The next value must be the sum of exactly one pair of the previous values in the sequence. Building the sequence:
    100 101
    100 101 201                         [next term is 101 + 100]
    100 101 201 301 302            [201 + each of previous two values]

    100 101 201 301 302
                                        401 402         502                   [301 plus previous]
                                                  402 403          503  603      [302 plus previous]
    100 101 201 301 302 401       403   502  503  603       [First 10 terms]

Sum of first 10 terms is: 3417