Arithmetic sequence involving years

AI Thread Summary
The discussion revolves around solving a problem related to an arithmetic sequence of houses built annually from 1986 to 2010. The key figures are 238 houses built in 2000 and 108 in 2010, leading to the calculation of the first year's output in 1986. The initial attempt at finding the number of houses built in 1986 resulted in an incorrect answer of 407, while the correct answer is 420, which requires adjusting the year count. Clarification on the year indexing reveals that 1986 should be considered as year n=1, leading to confusion about the arithmetic sequence calculations. Ultimately, understanding the correct year indexing is crucial for solving the problem accurately.
adjacent
Gold Member
Messages
1,552
Reaction score
62

Homework Statement


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

Homework Equations


##U_n = a + (n - 1)d##

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:
Physics news on Phys.org
There's a mistake in your work above.
 
rpthomps said:
There's a mistake in your work above.
Thanks. Fixed, but the question remains
 
adjacent said:

Homework Statement


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 from an arithmetic equation. Given that 238 houses were built in 2000 and 108 in 2010, find the number of houses built in 1986

Homework Equations


##U_n = a + (n - 1)d##

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?
Do you mean that
The number of houses built each year form an arithmetic progression (sequence).​
?Define what is meant by n .
 
SammyS said:
Do you mean that
The number of houses built each year form an arithmetic progression (sequence).​
?Define what is meant by n .
Fixed. Thanks.
n is the number of years starting from 1986
 
adjacent said:
Fixed. Thanks.
n is the number of years starting from 1986
So, is 1986 year n=1 or is it year n=0 ?
 
SammyS said:
So, is 1986 year n=1 or is it year n=0 ?
n=1
 
adjacent said:
n=1
In that case, n = year - 1985
 
SammyS said:
In that case, n = year - 1985
Can you explain? I do not understand
I have exams in half an hour D:
 
  • #10
adjacent said:
Can you explain? I do not understand
I have exams in half an hour D:
In other words, for the year 2000, n = 2000 -1985 = 15
 
  • #11
Thank god it did not come in exam

SammyS said:
In other words, for the year 2000, n = 2000 -1985 = 15
I know but why 1985 instead of 1986? The question says 1986 is the starting year
 
  • #12
adjacent said:
Thank god it did not come in examI know but why 1985 instead of 1986? The question says 1986 is the starting year
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.
 
  • Like
Likes adjacent
  • #13
SammyS said:
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.
I am so stupid. Thanks a lot. This was bugging me so hard last night.
 

Similar threads

Replies
7
Views
2K
2
Replies
67
Views
14K
Replies
7
Views
3K
Replies
9
Views
4K
Replies
5
Views
3K
Replies
7
Views
3K
Replies
7
Views
4K
Back
Top