SOLUTION: I've been trying to understand a solution by greenstamps here: https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1132971.html He g

Algebra ->  Sequences-and-series -> SOLUTION: I've been trying to understand a solution by greenstamps here: https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1132971.html He g      Log On


   

Question 1199753: I've been trying to understand a solution by greenstamps here:
https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1132971.html
He got me started by giving the rationale, but when I got to work on it, I didn't get the same answer as him and I have no idea why. Here's my work:
Q)
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
401 + 100 = 501 GOOD
301 + 201 = 502 BAD
302 + 201 = 503 GOOD
100, 101, 201, 301, 302, 401, 501, 503
501 + 100 = 601 GOOD
501 + 101 = 602 BAD
503 + 100 = 603 BAD
503 + 101 = 604 GOOD
100, 101, 201, 301, 302, 401, 501, 503, 601, 604
SUM = 3,615
Exactly 200 more than what he got.
Where am I wrong?
Please help. Thanks!


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


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.

And thanks for showing the work you did. It makes it very easy for me to help...!

Here is your work up to a certain point....

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

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.

Here is how those last few lines should look:

301 + 100 = 401 GOOD
301 + 101 = 402 BAD
101 + 302 = 403 GOOD
100, 101, 201, 301, 302, 401, 403

Then of course the subsequent numbers in the sequence will all be different.

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.