Moderate -0.8 Part (a) is a standard proof of the arithmetic series formula taught in C1, requiring only algebraic manipulation of S_n written forwards and backwards. Parts (b)-(d) are routine applications with simple arithmetic (finding a_5, S_5, and solving a quadratic). This is a textbook exercise testing basic recall and application with no problem-solving insight required, making it easier than average.
9. (a) Prove that the sum of the first \(n\) terms of an arithmetic series with first term \(a\) and common difference \(d\) is given by
$$\frac { 1 } { 2 } n [ 2 a + ( n - 1 ) d ] .$$
A novelist begins writing a new book. She plans to write 16 pages during the first week, 18 during the second and so on, with the number of pages increasing by 2 each week.
Find, according to her plan,
(b) how many pages she will write in the fifth week,
(c) the total number of pages she will write in the first five weeks.
(d) Using algebra, find how long it will take her to write the book if it has 250 pages.
9. (a) Prove that the sum of the first $n$ terms of an arithmetic series with first term $a$ and common difference $d$ is given by
$$\frac { 1 } { 2 } n [ 2 a + ( n - 1 ) d ] .$$
A novelist begins writing a new book. She plans to write 16 pages during the first week, 18 during the second and so on, with the number of pages increasing by 2 each week.
Find, according to her plan,\\
(b) how many pages she will write in the fifth week,\\
(c) the total number of pages she will write in the first five weeks.\\
(d) Using algebra, find how long it will take her to write the book if it has 250 pages.\\
\hfill \mbox{\textit{Edexcel C1 Q9 [12]}}