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Number Theory/Number Sequence


1(i)Find the nth term of the following sequence:
(ii)If the nth term is P, find 10^n in terms of P.

Hello Isabel

I fear you have missed out the fifth term, 0.  Without this there is no sense to the question.

So, for the sequence -0.5555, -0.555, -0.55, -.5, 0, 5, 55, 555, ...

Consider the eighth term.  It is the sum of a GP 5 + 5*10 + 5*10^3 = 5*(10^3 - 1)/9.

So the nth term is 5*(10^(n-5)-1)/9.  You can check this works.

If P = 5*(10^(n-5)-1)/9, 9P/5 = 10^(n-5)-1,  10^(n-5) = 9P/5+1 and 10^n = 10^5(1 + 9P/5)



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