CAIE P1 2016 March — Question 3 5 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2016
SessionMarch
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicArithmetic Sequences and Series
TypeFind term or common difference
DifficultyModerate -0.5 This is a straightforward two-equation problem using standard AP formulas (nth term and sum). Students substitute given values into a₁₂ = a + 11d = 17 and S₃₁ = 31/2(2a + 30d) = 1023, solve simultaneously for a and d, then find a₃₁. While it requires algebraic manipulation, it's a routine textbook exercise with no conceptual challenges—slightly easier than average due to its mechanical nature.
Spec1.04h Arithmetic sequences: nth term and sum formulae

3 The 12th term of an arithmetic progression is 17 and the sum of the first 31 terms is 1023. Find the 31st term.

Question 3:
AnswerMarks Guidance
AnswerMarks Guidance
\(a + 11d = 17\)B1
\(\dfrac{31}{2}(2a + 30d) = 1023\)B1
Solve simultaneous equationsM1
\(d = 4\), \(a = -27\)A1 At least one correct
31st term \(= 93\)A1 [5]
## Question 3:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $a + 11d = 17$ | B1 | |
| $\dfrac{31}{2}(2a + 30d) = 1023$ | B1 | |
| Solve simultaneous equations | M1 | |
| $d = 4$, $a = -27$ | A1 | At least one correct |
| 31st term $= 93$ | A1 [5] | |

---
3 The 12th term of an arithmetic progression is 17 and the sum of the first 31 terms is 1023. Find the 31st term.

\hfill \mbox{\textit{CAIE P1 2016 Q3 [5]}}