| Exam Board | Edexcel |
|---|---|
| Module | PURE |
| Year | 2024 |
| Session | October |
| Paper | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find term or total |
| Difficulty | Moderate -0.8 This is a straightforward application of standard arithmetic and geometric sequence formulas with clear scaffolding. Part (a) is direct substitution into the nth term formula, part (b) uses the sum formula for arithmetic series, and part (c) applies the geometric series sum formula. All required information is given explicitly, requiring only recall and careful arithmetic rather than problem-solving or insight. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
| Answer | Marks |
|---|---|
| 7(a) | ( u = ) 2 0 + 9 9 ( 0 . 5 ) = ( £ ) 6 9 . 5 0 * |
| 1 0 0 | B1* |
| Answer | Marks |
|---|---|
| (b) | 1 |
| Answer | Marks |
|---|---|
| 300 2 | M1 |
| = ( £ ) 2 8 4 2 5 | A1 |
| Answer | Marks |
|---|---|
| (c) | 2 5 0 |
| Answer | Marks |
|---|---|
| 2 0 | M1 |
| Answer | Marks |
|---|---|
| 2 8 4 2 5 − 2 7 3 6 2 . 9 4 8 . .. | M1 |
| (£)1060 | A1 |
Total 6
| Answer | Marks | Guidance |
|---|---|---|
| r | S | |
| 3 0 0 | Correct (b) − S |
| Answer | Marks | Guidance |
|---|---|---|
| 1.01 | 37576.93252… | 9151.932524… |
| 1.008 | 24796.03972… | 3628.960276… |
| 1.0085 | 27458.42195… | 966.5780531… |
| 1.00848 | 27345.9295… | 1079.070499… |
| 7 | 2189 |
Question 7:
--- 7(a) ---
7(a) | ( u = ) 2 0 + 9 9 ( 0 . 5 ) = ( £ ) 6 9 . 5 0 *
1 0 0 | B1*
(1)
(b) | 1
S = ( 3 0 0 ) 2 2 0 + 2 9 9 ( 0 . 5 ) = . . .
3 0 0 2
or
1
S = ( 300 ) 20+169.50 =...
300 2 | M1
= ( £ ) 2 8 4 2 5 | A1
(2)
(c) | 2 5 0
2 0 r 2 9 9 = 2 5 0 r = 2 9 9 ( = 1 . 0 0 8 4 8 3 0 3 2 . . ).
2 0 | M1
( )
20 1−r300
S = =( 27362.948... )
300 1−r
2 8 4 2 5 − 2 7 3 6 2 . 9 4 8 . .. | M1
(£)1060 | A1
(3)
Total 6
r | S
3 0 0 | |Correct (b) − S |
3 0 0
1.01 | 37576.93252… | 9151.932524…
1.008 | 24796.03972… | 3628.960276…
1.0085 | 27458.42195… | 966.5780531…
1.00848 | 27345.9295… | 1079.070499…
7 | 2189\begin{enumerate}
\item Jem pays money into a savings scheme, $A$, over a period of 300 months.
\end{enumerate}
Jem pays $\pounds 20$ into scheme $A$ in month $1 , \pounds 20.50$ in month $2 , \pounds 21$ in month 3 and so on, so that the amounts Jem pays each month form an arithmetic sequence.\\
(a) Show that Jem pays $\pounds 69.50$ into scheme $A$ in month 100\\
(b) Find the total amount that Jem pays into scheme $A$ over the period of 300 months.
Kim pays money into a different savings scheme, $B$, over the same period of 300 months.
In a model, the amounts Kim pays into scheme $B$ increase by the same percentage each month, so that the amounts Kim pays each month form a geometric sequence.
Given that Kim pays
\begin{itemize}
\item $\pounds 20$ into scheme $B$ in month 1
\item $\pounds 250$ into scheme $B$ in month 300\\
(c) use the model to calculate, to the nearest $\pounds 10$, the difference between the total amount paid into scheme $A$ and the total amount paid into scheme $B$ over the period of 300 months.
\end{itemize}
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\hfill \mbox{\textit{Edexcel PURE 2024 Q7}}