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## 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?

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