# Sequences & Series Question

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#1
So I am a little stuck on this question:

note that it is no calculator.

So here's my working so far, but can someone give me a hint? Am I supposed to just work out r numerically? surely not - the answer is r = 3 but how am I supposed to get it?
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#2
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#3
You can divide both sides by 11, if that helps - does it?
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2 years ago
#4
(Original post by Gmart)
You can divide both sides by 11, if that helps - does it?
The sum is actually

11th degree polynomials are extremely difficult to solve, and this one isn't so nice. Are you absolutely certain you can't use a calculator for this question, and that the non-calc icon could be a misprint?
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#5
The question is as given - the symbol means no calculator but if there is no way then I feel less stupid...
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2 years ago
#6
If r is a positive integer, then with a bit of approximation (rough logs) you could get an answer,
2 922 920 which has 7 digits
Divide by 11, the sum (r^12-1)/(r-1) has 6 digits. Note the first 12 terms goes up to r^11.
So r^2 ~ 10, so r~3.
Assuming integers, 3 is likely to be the solution and its possible to check by repeated multiplication by 9 up to 9^6 or by dividing the original by 11, multiplying by 2 and adding 1, then using the divisibility test for 3 or 9.
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