Edexcel C2 — Question 9 10 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks10
PaperDownload PDF ↗
TopicGeometric Sequences and Series
TypeCompound growth applications
DifficultyModerate -0.3 Part (a) is a standard bookwork proof of the geometric series formula that appears in every C2 textbook. Parts (b) and (c) are straightforward applications requiring only substitution into formulas with no problem-solving insight needed. The context is simple and the calculations routine, making this slightly easier than an average A-level question, though the 10-mark allocation and multi-part structure prevent it from being trivially easy.
Spec1.04i Geometric sequences: nth term and finite series sum

  1. A geometric series has first term \(a\) and common ratio \(r\). Prove that the sum of the first \(n\) terms of the series is $$\frac{a(1-r^n)}{1-r}.$$ [4]
Mr King will be paid a salary of £35 000 in the year 2005. Mr King's contract promises a 4% increase in salary every year, the first increase being given in 2006, so that his annual salaries form a geometric sequence.
  1. Find, to the nearest £100, Mr King's salary in the year 2008. [2]
Mr King will receive a salary each year from 2005 until he retires at the end of 2024.
  1. Find, to the nearest £1000, the total amount of salary he will receive in the period from 2005 until he retires at the end of 2024. [4]

\begin{enumerate}[label=(\alph*)]
\item A geometric series has first term $a$ and common ratio $r$. Prove that the sum of the first $n$ terms of the series is
$$\frac{a(1-r^n)}{1-r}.$$
[4]
\end{enumerate}

Mr King will be paid a salary of £35 000 in the year 2005. Mr King's contract promises a 4% increase in salary every year, the first increase being given in 2006, so that his annual salaries form a geometric sequence.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find, to the nearest £100, Mr King's salary in the year 2008.
[2]
\end{enumerate}

Mr King will receive a salary each year from 2005 until he retires at the end of 2024.

\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find, to the nearest £1000, the total amount of salary he will receive in the period from 2005 until he retires at the end of 2024.
[4]
\end{enumerate}

\hfill \mbox{\textit{Edexcel C2  Q9 [10]}}