Uri wrote:Ian Stewart wrote:Since we do not yet have a term in our sequence which is 250 or greater, we will never add a number as large as 0.2*250 = 50 to 200 to make a term - there will therefore never be a term as large as 250 in our sequence. The values will, however, get very close to 250. So after a2, every term is somewhere between 240 and 250.
Stewart, although I understand that the terms are gradually getting closer to 250, could you please explain the fundamental on which you told that the term will never cross 250?
I can try:
Say our sequence is a, b, c, d, e, f, g, ...
We know that we find the next term of our sequence by adding 20% of the previous term to 200. So if we know a, we'd find b by adding 20% of a and 200. Now, if a is less than 250, 20% of a must be less than 50, so b will be less than 250. If b is less than 250, then 20% of b will be less than 50, so c will be less than 250. And so on...
Hope that makes sense - it's probably easier to see if you start with 200 and find the next two or three terms; working out the first few terms is almost always a good idea in sequence questions.
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