You are here:

- Home
- Science
- Mathematics
- Number Theory
- Number Sequence

Advertisement

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

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.

Teacher of math for 53 years**Organizations**

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
**Publications**

Journal of mathematics and its applications
M500 magazine**Education/Credentials**

BSc (Hons) Liverpool (Science). BA (Hons) OU (Mathematics)**Awards and Honors**

State Scholarship 1955
Highest Score in Yorkshire on OU course MST209 £50 prize
First class honours in OU BA Mathematics**Past/Present Clients**

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.