| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2018 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | New GP from transformation |
| Difficulty | Moderate -0.3 This is a multi-part question covering standard A-level topics (geometric series convergence, GP properties, compound interest). Part (a) is basic recall, part (b) requires algebraic manipulation of sum to infinity formulas but follows a predictable pattern, and part (c) is a routine compound interest calculation with geometric series. The 'show that W is a GP' is straightforward (squaring terms gives common ratio r²). Overall slightly easier than average due to standard techniques and clear structure, though the 10 marks total suggests some working is required. |
| Spec | 1.04j Sum to infinity: convergent geometric series |r|<11.04k Modelling with sequences: compound interest, growth/decay |
\begin{enumerate}[label=(\alph*)]
\item Explain why the sum to infinity of a geometric series with common ratio $r$ only converges when $|r| < 1$. [1]
\item A geometric progression $V$ has first term 2 and common ratio $r$. Another progression $W$ is formed by squaring each term in $V$. Show that $W$ is also a geometric progression. Given that the sum to infinity of $W$ is 3 times the sum to infinity of $V$, find the value of $r$. [6]
\item At the beginning of each year, a man invests £5000 in a savings account earning compound interest at the rate of 3% per annum. The interest is added at the end of each year. Find the total amount of his savings at the end of the 20th year correct to the nearest pound. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2018 Q9 [10]}}