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# Number Theory/Number Sequence

Question
1(i)Find the nth term of the following sequence:
-0.5555,-0.555,-0.55,-0.5,5,55,555,...
(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)

Regards

vijilant

Number Theory

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#### Vijilant

##### Expertise

Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.

##### Experience

Teacher of math for 53 years

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AQA Doncaster Bridge Club Danum Strings Orchestra Doncaster Conservative Club Danum Strings Orchestra Simply Voices Choir Doncaster TNS mystery shopping St Paul's Music Group Cantley

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Journal of mathematics and its applications M500 magazine

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BSc (Hons) Liverpool (Science). BA (Hons) OU (Mathematics)

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State Scholarship 1955 Highest Score in Yorkshire on OU course MST209 £50 prize First class honours in OU BA Mathematics

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I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things. One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.