John G.

asked • 01/24/17

Notice numbers/sum in sequence

In the sequence 1,4,v,6,7,8,10,sixteen,xviii,... each number after the first ii is the next number that can be expressed as the sum of two previous numbers in but i manner. For example,ten 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 ten+5 and 8+7 equal 15. In a like sequence that begins with the two numbers 100 and 101, the sum of the first ten terms is

I have no inkling how to do this, please help

1 Expert Respond

The sequence begins with 100, 101.

The next value must be the sum of exactly ane 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 2 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

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