| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Find term or common difference |
| Difficulty | Moderate -0.8 This is a straightforward arithmetic progression question requiring standard formula application: setting up two equations from given information (a+8d=22 and S₄=49), solving simultaneously for a and d, then using the nth term formula. It involves routine algebraic manipulation with no conceptual challenges or novel problem-solving, making it easier than average but not trivial due to the simultaneous equations step. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| \(a + 8d = 22\) | B1 | co |
| \(2(2a + 3d) = 49\) | B1 | co |
| Solution of sim eqns \(\rightarrow d = 1.5,\ a = 10\) | M1 A1 [4] | Solution of two linear sim eqns. co |
| Answer | Marks | Guidance |
|---|---|---|
| \(a + (n-1)d = 46\), substitutes for \(a\) and \(d\), \(\rightarrow n = 25\) | M1 A1 [2] | Correct formula needed and attempt to solve. co |
## Question 3:
$9^{\text{th}}$ term $= 22$, $S_4 = 49$
**Part (i):**
$a + 8d = 22$ | B1 | co
$2(2a + 3d) = 49$ | B1 | co
Solution of sim eqns $\rightarrow d = 1.5,\ a = 10$ | M1 A1 [4] | Solution of two linear sim eqns. co
**Part (ii):**
$a + (n-1)d = 46$, substitutes for $a$ and $d$, $\rightarrow n = 25$ | M1 A1 [2] | Correct formula needed and attempt to solve. co
---3 The ninth term of an arithmetic progression is 22 and the sum of the first 4 terms is 49 .\\
(i) Find the first term of the progression and the common difference.
The $n$th term of the progression is 46 .\\
(ii) Find the value of $n$.
\hfill \mbox{\textit{CAIE P1 2010 Q3 [6]}}