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The number of apartments in a housing development has been increasing by a constant amount every year. At the end of the first year, the number of apartments was {u_1}, and at the end of the {years} year, the number of apartments was {u_years}. The number of apartments, $y$, can be determined by the equation $y = mt + n$,  where $t$ is the time, in years.

", "advice": "

$m$ is the gradient of the line, it is also the common difference in the arithmetic sequence so you can use the formula $u_n = u_1 + (n-1)d$

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In this case $n =$  {n} so {u_years} = {u_1} + ({n}-1) $\\times d$ 

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m = {u_years - u_1} $\\div$ {n-1}

\n

m = {d}

\n

$n$ represents the situation at the beginning of year 1, so is $u_1 - d$

\n

$n =$ {u_1} - {d}

\n

$n =$ {u_0}

\n

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first term (houses at end of first year)

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conversion list for number of years to english

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number of years at which second number of houses is given

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n converted to word

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u_n number of houses after n years

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common difference to apply

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first term of sequence (houses at start of first year)

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Find the value of $m$.

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Find the value of $n$.

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