You are here:

Number Theory/Number Sequence

Advertisement


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.

Answer
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

All Answers


Answers by Expert:


Ask Experts

Volunteer


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

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.

©2016 About.com. All rights reserved.