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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 $u_n = u_1 + (n-1)d$
\nIn this case $n =$ {n} so {u_years} = {u_1} + ({n}-1) $\\times d$
\nm = {u_years - u_1} $\\div$ {n-1}
\nm = {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", "rulesets": {}, "extensions": [], "variables": {"u_1": {"name": "u_1", "group": "Ungrouped variables", "definition": "{u_0}+d", "description": "first term (houses at end of first year)
", "templateType": "anything"}, "years_eng": {"name": "years_eng", "group": "Ungrouped variables", "definition": "[ \"first\", \"second\", \"third\", \"fourth\", \"fifth\", \"sixth\", \"seventh\", \"eighth\", \"ninth\", \"tenth\" ]", "description": "conversion list for number of years to english
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", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(60 .. 110#10)", "description": "common difference to apply
", "templateType": "randrange"}, "u_0": {"name": "u_0", "group": "Ungrouped variables", "definition": "random(40 .. 120#10)", "description": "first term of sequence (houses at start of first year)
", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["u_1", "years_eng", "n", "years", "u_years", "d", "u_0"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Find the value of $m$.
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