My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum

LinkBack Thread Tools Display Modes
January 6th, 2016, 03:48 AM   #1
Joined: Mar 2015
From: KY

Posts: 35
Thanks: 1

Finding the nth term in a fractional sequence

Could someone help me with the process of figuring out # 25?

scsims is offline  
January 6th, 2016, 04:56 AM   #2
Joined: Jan 2016
From: Ghana

Posts: 17
Thanks: 4

It can be observed that the denominators are powers of 3 in ascending order and the numerator seem to also be increasing in ascending powers of 2 so we can assume it is a geometric progression. Divide the 2nd term by the first.
Divide the 3rd by the 2nd to verify the ratio
Hence we can assume it is a geometric sequence with a common ratio 2/3 and a first term 1/3. Although we cannot be entirely sure until we have enough terms of the sequence. However if we assume that it is geometric, then we can substitute into the formula
u(n)=ar^(n-1), where u(n) is the nth term, a is the first term and r is the common ratio. We just substitute n=24 and n=26 and divide the result of u(24) by u(26) to find the quotient
Lanthanide is offline  
January 6th, 2016, 05:22 AM   #3
Joined: Mar 2015
From: KY

Posts: 35
Thanks: 1

So u(n) is the nth term?

I'm a little confused, what is u?

Is this the problem that need to be solved for the 24th term?
scsims is offline  
January 6th, 2016, 07:30 AM   #4
Math Team
Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

Lanthanide said "where u(n) is the nth term" of the sequence. As for "what is u?" there is no "u". There are only terms of the sequence, u(0), u(1), etc..

By the way, to "find the quotient if the 24th term is divided by the 26th term", you do NOT need to actually find the 24th and 26th terms. The reason this is a "geometric sequence" is that any term divided by the next term is 2/3. The 24th term divided by the 25th term is 2/3 and the 25th term divided by the 26th term is 2/3. The "24th term divided by the 26th term" is $\displaystyle \frac{u(24)}{u(26)}= \frac{u(24)}{u(25)}\frac{u(25)}{u(26)}$.

Last edited by Country Boy; January 6th, 2016 at 07:36 AM.
Country Boy is offline  
January 6th, 2016, 11:32 AM   #5
Math Team
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,290
Thanks: 1023

nth term = a * [m^(n-1)]

a = 1/3, m = 2/3, n = 24, 26

24th / 26th =

Denis is offline  

  My Math Forum > High School Math Forum > Algebra

finding, fractional, nth, sequence, term

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Trying to figure out formula for nth term of this sequence jonas Pre-Calculus 4 July 19th, 2017 05:28 PM
Finding a term in a graphing sequence. johnny010 Calculus 1 September 14th, 2015 03:51 AM
General term of a sequence Aaron Real Analysis 6 March 17th, 2015 05:06 PM
I discovered a formula for the nth term of any sequence karpmage Number Theory 11 February 21st, 2013 04:42 AM
general or nth term of a sequence emohbe Algebra 1 December 14th, 2010 12:16 AM

Copyright © 2019 My Math Forum. All rights reserved.