| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2017 |
| Session | October |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find term or total |
| Difficulty | Moderate -0.8 This is a straightforward arithmetic sequence question requiring only direct application of standard formulas (nth term and sum). Part (a) is a simple linear equation, part (b) uses the sum formula with given values, and part (c) equates two sums. All steps are routine with no problem-solving insight needed, making it easier than average but not trivial due to the multi-part structure. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Uses \(1000 = 600 + 80(N-1) \Rightarrow N = 6\) | M1 | Attempts to use \(u_n = a + (n-1)d\) to find value of \(n\); evidence would be \(1000 = 600 + 80(N-1)\); alternatively attempts \(\frac{1000-600}{80}+1\) or repeated addition of £80 onto £600 until £1000 is reached |
| \(N = 6\) | A1 | Accept "the 6th year" or similar; answer alone scores both marks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Uses \(\frac{15}{2}(2\times600+(15-1)\times80) = \text{(£)}17400\) | M1 | Uses correct sum formula \(S = \frac{n}{2}(2a+(n-1)d)\) with \(n=15, a=600, d=80\); alternatively \(S=\frac{n}{2}(a+l)\) with \(l=600+14\times80=1720\); accept sum of 15 terms starting \(600+680+760+840+\ldots\) |
| \((£)17400\) | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Total for Saima \(= \frac{15}{2}(2A+14A) = 120A\) | B1 | Finds sum for Saima; accept unsimplified forms \(\frac{15}{2}(2A+14A)\) or \(\frac{15}{2}(A+15A)\) or simplified \(120A\); isw following correct answer |
| Sets \(120A = 17400 \Rightarrow A = 145\) | M1 | Sets their \(120A\) equal to answer from (b); must attempt sums not terms |
| \(A = 145\) | A1 | cao |
## Question 6:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Uses $1000 = 600 + 80(N-1) \Rightarrow N = 6$ | M1 | Attempts to use $u_n = a + (n-1)d$ to find value of $n$; evidence would be $1000 = 600 + 80(N-1)$; alternatively attempts $\frac{1000-600}{80}+1$ or repeated addition of £80 onto £600 until £1000 is reached |
| $N = 6$ | A1 | Accept "the 6th year" or similar; answer alone scores both marks |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Uses $\frac{15}{2}(2\times600+(15-1)\times80) = \text{(£)}17400$ | M1 | Uses correct sum formula $S = \frac{n}{2}(2a+(n-1)d)$ with $n=15, a=600, d=80$; alternatively $S=\frac{n}{2}(a+l)$ with $l=600+14\times80=1720$; accept sum of 15 terms starting $600+680+760+840+\ldots$ |
| $(£)17400$ | A1 | cao |
### Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Total for Saima $= \frac{15}{2}(2A+14A) = 120A$ | B1 | Finds sum for Saima; accept unsimplified forms $\frac{15}{2}(2A+14A)$ or $\frac{15}{2}(A+15A)$ or simplified $120A$; isw following correct answer |
| Sets $120A = 17400 \Rightarrow A = 145$ | M1 | Sets their $120A$ equal to answer from (b); must attempt sums not terms |
| $A = 145$ | A1 | cao |
---\begin{enumerate}
\item Each year Lin pays into a savings scheme. In year 1 she pays in $\pounds 600$. Her payments then increase by $\pounds 80$ a year, so that she pays $\pounds 680$ into the savings scheme in year $2 , \pounds 760$ in year 3 and so on. In year $N$, Lin pays $\pounds 1000$ into the savings scheme.\\
(a) Find the value of $N$.\\
(b) Find the total amount that Lin pays into the savings scheme from year 1 to year 15 inclusive.
\end{enumerate}
Saima starts paying into a different savings scheme at the same time as Lin starts paying into her savings scheme.
In year 1 she pays in $\pounds A$. Her payments increase by $\pounds A$ each year so that she pays $\pounds 2 A$ in year $2 , \pounds 3 A$ in year 3 and so on.
Given that Saima and Lin have each paid, in total, the same amount of money into their savings schemes after 15 years,\\
(c) find the value of $A$.
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\hfill \mbox{\textit{Edexcel C12 2017 Q6 [7]}}