Results 1 to 4 of 4

Math Help - couple of questions...

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    21

    couple of questions...

    I have a couple of questions that have got me bugged for a while...

    1)Find the sum of the arithmetic progression 1, 4, 7, 10, 13, 16... , 1000.
    (already figured that part out to be 167167, with 334 terms)

    Every third term of the progression above is removed, i. e. 7, 16, etc. Find The sum of the remaining terms.

    I figured that I'd just find the sum of the terms removed, then substract that from 167167, except for the fact that I don't know the number of terms are in the sequence. Any ideas?

    2)The binomial expansion of (1+ax)^n, where n is a positive integer, has six terms. The coefficent of the x^3 term is 5/4. Find a.

    I know that n=5, but the rest is a mystery to me algebraically. I did it using Pascal's Triangle, but I want to know how to do it a quicker way.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,315
    Thanks
    1225
    Quote Originally Posted by DemonX01 View Post
    2)The binomial expansion of (1+ax)^n, where n is a positive integer, has six terms. The coefficent of the x^3 term is 5/4. Find a.

    I know that n=5, but the rest is a mystery to me algebraically. I did it using Pascal's Triangle, but I want to know how to do it a quicker way.
    (1 + ax)^5 = \sum_{r = 0}^5{5\choose{r}}(1)^{5 - r}(ax)^r

     = \sum_{r = 0}^5{5\choose{r}}a^rx^r.


    The x^3 term will be of the form

    {5\choose{3}}a^3x^3

    so its coefficient is

    {5\choose{3}}a^3.


    You should know that {5\choose{3}} = 10.


    And since this coefficient is \frac{5}{4}, then you have

    10a^3 = \frac{5}{4}

    a^3 = \frac{1}{8}

    a = \frac{1}{2}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,306
    Thanks
    1282
    Quote Originally Posted by DemonX01 View Post
    I have a couple of questions that have got me bugged for a while...

    1)Find the sum of the arithmetic progression 1, 4, 7, 10, 13, 16... , 1000.
    (already figured that part out to be 167167, with 334 terms)

    Every third term of the progression above is removed, i. e. 7, 16, etc. Find The sum of the remaining terms.

    I figured that I'd just find the sum of the terms removed, then substract that from 167167, except for the fact that I don't know the number of terms are in the sequence. Any ideas?
    You should have written down a couple more steps: 7, 16, 25, 34,..., 997 is an arithmetic sequence with common difference 9 (because every third step is 3+ 3+ 3= 9). There are, of course, 333/3= 111 terms in that sequence.

    2)The binomial expansion of (1+ax)^n, where n is a positive integer, has six terms. The coefficent of the x^3 term is 5/4. Find a.

    I know that n=5, but the rest is a mystery to me algebraically. I did it using Pascal's Triangle, but I want to know how to do it a quicker way.[/QUOTE]
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jan 2010
    Posts
    21
    Quote Originally Posted by HallsofIvy View Post
    You should have written down a couple more steps: 7, 16, 25, 34,..., 997 is an arithmetic sequence with common difference 9 (because every third step is 3+ 3+ 3= 9). There are, of course, 333/3= 111 terms in that sequence.
    [/quote]

    Could you explain that part more? How did you arrive at 997 as being the final term?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help with a couple of questions
    Posted in the Algebra Forum
    Replies: 7
    Last Post: September 25th 2011, 09:27 AM
  2. [SOLVED] A couple questions...Help please.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: July 24th 2010, 05:05 PM
  3. A couple of Questions.
    Posted in the Geometry Forum
    Replies: 5
    Last Post: April 8th 2009, 09:54 AM
  4. a couple of questions...thanks
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: April 12th 2008, 08:18 PM
  5. Couple of questions
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: September 20th 2007, 05:28 AM

Search Tags


/mathhelpforum @mathhelpforum