Results 1 to 2 of 2

Thread: Compressing a curve/sequence of numbers

  1. #1
    Newbie
    Joined
    Mar 2017
    From
    UK
    Posts
    1

    Compressing a curve/sequence of numbers

    [Apologies if this is in the wrong sub-forum as my maths knowledge is not much more than basic]


    Here is a sequence of numbers, starting at 1 and then doubling at each step until 128 is reached. It would produce a nice curve if plotted on a graph.


    I - 1
    II - 2
    III - 4
    IV - 8
    V - 16
    VI - 32
    VI - 64
    VIII - 128


    If I wanted to reduce the sequence of numbers from eight to five, while retaining the curve and keeping the first and final numbers of the sequence the same, how would I calculate this?


    So compressing it like this:


    I - 1
    II - ?
    III - ?
    IV - ?
    V - 128


    Also, while I am here, how would one calculate stretching the sequence in the perpendicular direction? So keeping a sequence of eight numbers this time, with 1 remaining as 1 and the final number (VIII) being diminished from 128 to, for instance, 100 and the curve adjusting relative to it?

    So like this:

    I - 1
    II - ?
    III - ?
    IV - ?
    V - ?
    VI - ?
    VI - ?
    VIII - 100

    Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,594
    Thanks
    2359

    Re: Compressing a curve/sequence of numbers

    your first sequence is

    $a_n = 2^n,~n=0,1,2,\dots$

    now you want to make a new sequence $b$ such that

    $b_n=1,~b_5=128$

    ok, let's assume the same form as the first sequence just with a different base

    $b_n = \beta^n$

    $b_0 = \beta^0 = 1$ so we're good there

    $b_5 = \beta^5 = 128$

    $\beta = (128)^{1/5} \approx 2.64$

    $b_n = \left((128)^{1/5}\right)^n = (128)^{n/5}$

    same deal for your 2nd problem

    $c_n = \gamma^n$

    $c_5 = \gamma^5 = 100$

    $\gamma = (100)^{1/5}$

    $c_n = (100)^{n/5}$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Stretching and Compressing Functions
    Posted in the Algebra Forum
    Replies: 5
    Last Post: Mar 13th 2017, 09:15 AM
  2. sum of odd numbers in sequence
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Feb 24th 2017, 03:48 PM
  3. Principle behind compressing trig functions
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 10th 2013, 05:32 AM
  4. Sequence of numbers
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: Sep 28th 2011, 05:40 AM
  5. what are the next 2 numbers in the sequence?
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Jun 13th 2009, 05:24 AM

/mathhelpforum @mathhelpforum