Question 1041280: What will be the next number and how?
73, 298, 475, 544,688,
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
List them in a column:
73
298
475
544
688
Subtract each number from the number just below it
and write it out to the right in a second column:
73 225
298 177
475 69
544 144
688
Subtract each number from the number just below it
and write it out to the right in a third column:
73 225 -48
298 177 -108
475 69 75
544 144
688
Subtract each number from the number just below it
and write it out to the right in a fourth column:
73 225 -48 -60
298 177 -108 183
475 69 75
544 144
688
Subtract that number from the number just below it
and write it out to the right in a fifth column:
73 225 -48 -60 243
298 177 -108 183
475 69 75
544 144
688
Now put another 243 under that one on the end,
and now we'll work backwards to the first column.
73 225 -48 -60 243
298 177 -108 183 243
475 69 75
544 144
688
Add 243 to the 183 just left of it, getting 426
and write it under the 183
73 225 -48 -60 243
298 177 -108 183 243
475 69 75 426
544 144
688
Add the 426 to the 75 just left of it, getting 501,
and write it under the 75
73 225 -48 -60 243
298 177 -108 183 243
475 69 75 426
544 144 501
688
Add the 501 to the 144 just left of it, getting 645,
and write it under the 144.
73 225 -48 -60 243
298 177 -108 183 243
475 69 75 426
544 144 501
688 645
Finally add the 645 to the 688 just left of it, getting 1333,
and write it under the 688.
73 225 -48 -60 243
298 177 -108 183 243
475 69 75 426
544 144 501
688 645
1333
The next number is 1333.
Edwin
Answer by ikleyn(52790)  (Show Source):
You can put this solution on YOUR website! .
What will be the next number and how?
73, 298, 475, 544,688,
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If to blindly follow to this logic (to the previous solution), then you quickly come to the conclusion
that for every sequence of five numbers the sixth term is uniquely predefined.
For me, it is much better to say to the sender, that such problem, as it is formulated, doesn't make sense.
Although the technique demonstrated of that solution was perfect.
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