| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2022 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Shared terms between AP and GP |
| Difficulty | Standard +0.8 This question requires setting up simultaneous equations from AP and GP conditions, algebraic manipulation to derive a quartic equation, then solving it and applying GP sum formula. While systematic, it demands careful algebra across multiple steps, connecting two progression types, and solving a quartic (factorable as quadratic in y²). The derivation in part (a) requires non-trivial manipulation, making this moderately challenging but still within standard A-level techniques. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
The positive integers $x$, $y$ and $z$ are the first, second and third terms, respectively, of an arithmetic progression with common difference $-4$.
Also, $x$, $\frac{15}{y}$ and $z$ are the first, second and third terms, respectively, of a geometric progression.
\begin{enumerate}[label=(\alph*)]
\item Show that $y$ satisfies the equation $y^4 - 16y^2 - 225 = 0$. [4]
\item Hence determine the sum to infinity of the geometric progression. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2022 Q4 [8]}}