| Exam Board | Edexcel |
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| Module | PMT Mocks (PMT Mocks) |
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| Topic | Arithmetic Sequences and Series |
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13. A construction company had a 30 -year programme to build new houses in Newtown. They began in the year 1991 (Year 1) and finished in 2020 (Year 30).
The company built 120 houses in year 1, 140 in year 2, 160 houses in year 3 and so on, so that the number of houses they built form an arithmetic sequence.
A total of 8400 new houses were built in year \(n\).
a. Show that
$$n ^ { 2 } + 11 n - 840 = 0$$
b. Solve the equation
$$n ^ { 2 } + 11 n - 840 = 0$$
and hence find in which year 8400 new houses were built.