Moderate -0.3 This is a straightforward arithmetic sequence problem requiring students to form and solve a quadratic equation. Part (a) involves setting up the sum formula Sn = n/2[2a + (n-1)d] with given values (a=120, d=20, Sn=8400) and simplifying to the required form—a routine algebraic manipulation. Part (b) is standard quadratic solving. The question is slightly easier than average because it's highly scaffolded (the equation is given in part a) and uses standard textbook techniques with no novel insight required.
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.
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.\\
\hfill \mbox{\textit{Edexcel PMT Mocks Q13 [4]}}