Results 1 to 6 of 6

Math Help - Arthimetic Series 1

  1. #1
    Member
    Joined
    Feb 2013
    From
    Canada
    Posts
    131

    Exclamation Arthimetic Series 1

    1. It's About Time, in Langley, British Columbia, is Canada's largest custom clock manufacturer. They have a grandfather clock that, on the hours, chimes to the time of day. For example, at 4:00 PM, it chimes 4 times. How many times does the clock chime in a 24-h period?

    I tried using the formula Sn = n/2(t1 + tn) and Tn = T1 + (n - 1)d

    This is what I did:

    Tn = T1 + (n - 1)d

    Tn = 1 + (24 - 1)1

    Tn = 24

    I plugged in 1 for T1 because I assume the first time is 1 PM... I put 24 for n (n = number of terms) because 24 is how many hours there are. And I plugged in 1 for d because I guess the difference is 1.

    Sn = n/2(t1 + tn)

    S24 = 24/2 (1 + 24)

    I plugged in 24 for n (number of terms), 1 for first term, and 24 for tn.

    What I did was wrong, and I don't know what to do here...

    The correct answer is 156 times.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    828
    Thanks
    209

    Re: Arthimetic Series 1

    The series becomes 1+2+3+4+5+.....+ 24
    a = 1 n=24 d = 1: Sn = n/2 [ 2a + (n-1) d ] or sum of n natural numbers isgiven by n(n+1)/2
    so we get S24 = 24 ( 24+1)/2 = 24*25/2= 12*25 = 300
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Feb 2013
    From
    Saudi Arabia
    Posts
    440
    Thanks
    86

    Re: Arthimetic Series 1

    the answer is 300 as ibdutt found and not 156.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Feb 2013
    From
    Canada
    Posts
    131

    Re: Arthimetic Series 1

    This is a question from a math textbook and I have the answer key, the correct answer to this question is 156 times, not 300 times.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    828
    Thanks
    209

    Re: Arthimetic Series 1

    I am sorry for I read the question wrong. It is given that it chimes 4 times at 4 pm whereas I took it as if the clock chimes 16 times at 4 pm.
    Now in the light of this revelation the question is simple that it chimes from 1 to 12 times for am and 1 to 12 times for pm.
    Thus total number of times for first 12 hours would be 12/2[ 2 + ( 12-1) *1] = 6* 13 = 78 and same number for next 12 hours thus total number would be 78*2 = 156.
    Once again sorry for wrong interpretation.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Feb 2013
    From
    Canada
    Posts
    131

    Re: Arthimetic Series 1

    Thank you! I understand now.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: May 22nd 2012, 05:57 AM
  2. Replies: 3
    Last Post: September 29th 2010, 06:11 AM
  3. Replies: 0
    Last Post: January 26th 2010, 08:06 AM
  4. Is this right? (modular arthimetic)
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: January 15th 2010, 10:03 AM
  5. Replies: 1
    Last Post: May 5th 2008, 09:44 PM

Search Tags


/mathhelpforum @mathhelpforum