CAIE P1 2021 June — Question 2 5 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicArithmetic Sequences and Series
TypeFind term or common difference
DifficultyStandard +0.3 This is a straightforward application of the arithmetic series formula S_n = n/2[2a + (n-1)d]. Students form two equations from the given sums, solve simultaneously for a and d, then find the 60th term using a + 59d. While it requires multiple steps and algebraic manipulation, it's a standard textbook exercise with no novel insight required, making it slightly easier than average.
Spec1.04h Arithmetic sequences: nth term and sum formulae
2 The sum of the first 20 terms of an arithmetic progression is 405 and the sum of the first 40 terms is 1410 . Find the 60th term of the progression.
Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
\(10(2a + 19d) = 405\)B1
\(20(2a + 39d) = 1410\)B1
Solving simultaneously two equations obtained from using the correct sum formulae \([a = 6, \ d = 1.5]\)M1 Reach \(a =\) or \(d =\)
Using the correct formula for 60th term with their \(a\) and \(d\)M1
60th term \(= 94.5\)A1 OE, e.g. \(\frac{189}{2}\)
5 
**Question 2:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| $10(2a + 19d) = 405$ | B1 | |
| $20(2a + 39d) = 1410$ | B1 | |
| Solving simultaneously two equations obtained from using the correct sum formulae $[a = 6, \ d = 1.5]$ | M1 | Reach $a =$ or $d =$ |
| Using the correct formula for 60th term with their $a$ and $d$ | M1 | |
| 60th term $= 94.5$ | A1 | OE, e.g. $\frac{189}{2}$ |
| | **5** | |
2 The sum of the first 20 terms of an arithmetic progression is 405 and the sum of the first 40 terms is 1410 .

Find the 60th term of the progression.\\

\hfill \mbox{\textit{CAIE P1 2021 Q2 [5]}}
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Q1 4 Q2 5 Q3 6 Q4 3 Q5 4 Q6 5 Q7 5 Q8 10 Q9 11 Q10 8 Q11 14