Question 1199753
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Thanks for re-posting.  It is very seldom that I get to see that a student whom I have tried to help has taken my suggestions and tried to finish the problem himself.<br>
And thanks for showing the work you did.  It makes it very easy for me to help...!<br>
Here is your work up to a certain point....<br>
100, 101
100 + 101 = 201
100, 101, 201
201 + 100 = 301
201 + 101 = 302
100, 101, 201, 301, 302
301 + 100 = 401 GOOD
301 + 101 = 402 BAD
100, 101, 201, 301, 302, 401<br>
You missed one there.  Easy to do, since it is an unfamiliar process you have to go through to find the next numbers in the sequence.<br>
Here is how those last few lines should look:<br>
301 + 100 = 401 GOOD
301 + 101 = 402 BAD
101 + 302 = 403 GOOD
100, 101, 201, 301, 302, 401, 403<br>
Then of course the subsequent numbers in the sequence will all be different.<br>
Note that the units digits of the subsequent numbers in the sequence will all still be the same; and the tens digits are all still 0.  So your list of the first ten terms of the sequence, compared to the corrected list, will have one fewer number in the 400s and one more number in the 600s, with the tens and units digits in both lists being the same -- making the difference between your sum and the correct sum exactly 200.<br>