1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Arithmetic sequence involving years

Tags:
  1. May 24, 2016 #1

    adjacent

    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data
    A 25 year old programme for building new houses began in Core Town in the year 1986 and finished in 2010.

    The number of houses built each year form an arithmetic sequence. Given that 238 houses were built in 2000 and 108 in 2010, find the number of houses built in 1986

    2. Relevant equations
    ##U_n = a + (n - 1)d##

    3. The attempt at a solution
    ##d = \frac{108 - 238}{10} = -13##
    ##238 = a + ((2000- 1986) - 1) * -13##
    ##a = 407##

    But the real answer is ##a=420## by adding 1 to the 2000-1968. I do not understand why.
    Can someone enlighten me?
     
    Last edited: May 24, 2016
  2. jcsd
  3. May 24, 2016 #2
    There's a mistake in your work above.
     
  4. May 24, 2016 #3

    adjacent

    User Avatar
    Gold Member

    Thanks. Fixed, but the question remains
     
  5. May 24, 2016 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Do you mean that
    The number of houses built each year form an arithmetic progression (sequence).​
    ?


    Define what is meant by n .
     
  6. May 24, 2016 #5

    adjacent

    User Avatar
    Gold Member

    Fixed. Thanks.
    n is the number of years starting from 1986
     
  7. May 24, 2016 #6

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    So, is 1986 year n=1 or is it year n=0 ?
     
  8. May 24, 2016 #7

    adjacent

    User Avatar
    Gold Member

    n=1
     
  9. May 24, 2016 #8

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    In that case, n = year - 1985
     
  10. May 24, 2016 #9

    adjacent

    User Avatar
    Gold Member

    Can you explain? I do not understand
    I have exams in half an hour D:
     
  11. May 24, 2016 #10

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    In other words, for the year 2000, n = 2000 -1985 = 15
     
  12. May 25, 2016 #11

    adjacent

    User Avatar
    Gold Member

    Thank god it did not come in exam

    I know but why 1985 instead of 1986? The question says 1986 is the starting year
     
  13. May 25, 2016 #12

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Well, as you said, for the year 1986 n should be 1. 1986 - 1986 = 0, not 1.

    1987 should give n = 2, right? But 1987 - 1986 = 1 not 2. Etc.
     
  14. May 25, 2016 #13

    adjacent

    User Avatar
    Gold Member

    I am so stupid. Thanks a lot. This was bugging me so hard last night.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Arithmetic sequence involving years
  1. Arithmetic sequences (Replies: 5)

  2. Arithmetic Sequence (Replies: 2)

  3. Arithmetic Sequence (Replies: 1)

  4. Arithmetic Sequence (Replies: 5)

  5. Arithmetic Sequence (Replies: 4)

Loading...