Pure: Sequences and Series (incl. Binomial Expansion): Fluency and Exam Drill - Worksheets, Questions and Revision

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A-Level · Pure Mathematics

P4D Pure: Sequences and Series (incl. Binomial Expansion): Fluency and Exam Drill

EDEXCEL 9MA0 · Calculator allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

An arithmetic sequence has first term 5 and common difference 3. Find the 10th term.

(Total for Question 1 is 1 mark)

An arithmetic sequence has first term 40 and common difference -3. Find the 6th term.

(Total for Question 2 is 1 mark)

A geometric sequence has first term 4 and common ratio 3. Find the 4th term.

(Total for Question 3 is 1 mark)

A geometric sequence has first term 100 and common ratio 0.5. Find the 3rd term.

(Total for Question 4 is 1 mark)

Write down the value of 5C2 (5 choose 2).

(Total for Question 5 is 1 mark)

Write down the coefficient of x in the expansion of (1+x)⁷.

(Total for Question 6 is 1 mark)

An arithmetic series has first term 2 and common difference 5. Find the sum of the first 4 terms.

(Total for Question 7 is 1 mark)

A geometric series has first term 3 and common ratio 2. Find the sum of the first 4 terms.

(Total for Question 8 is 1 mark)

A geometric series has first term 20 and common ratio 0.5. State the sum to infinity.

(Total for Question 9 is 1 mark)

Write down the first two terms, in ascending powers of x, of the binomial expansion of (1+x)⁹.

(Total for Question 10 is 1 mark)

An arithmetic sequence has 3rd term 17 and common difference 4. Find the first term.

(Total for Question 11 is 2 marks)

Find the sum of the first 20 positive integers (1 + 2 + 3 + ... + 20).

(Total for Question 12 is 2 marks)

Find the coefficient of x² in the expansion of (1+3x)⁵.

(Total for Question 13 is 2 marks)

An arithmetic series has first term 8 and 20th term 84. Find the common difference, and find the sum of the first 20 terms.

(Total for Question 14 is 3 marks)

A geometric sequence has first term 6 and 4th term 162. Find the common ratio, and find the 6th term.

(Total for Question 15 is 3 marks)

Find the sum of the first 15 terms of the arithmetic series 7 + 11 + 15 + ...

(Total for Question 16 is 3 marks)

Find the coefficient of x³ in the expansion of (2+x)⁶, giving your answer as an integer.

(Total for Question 17 is 3 marks)

A company's sales form an arithmetic sequence. In month 1, sales are 150 units, and sales increase by 12 units each month. Find the total sales over the first 24 months.

(Total for Question 18 is 4 marks)

A geometric series has first term a = 54 and sum to infinity 81. Find the common ratio r, and find the sum of the first 5 terms, giving your answer to 3 significant figures.

(Total for Question 19 is 4 marks)

The first three terms of an arithmetic sequence, in order, are k - 2, 2k + 1 and 5k - 4, where k is a constant. Find the value of k, and hence find the common difference of the sequence.

(Total for Question 20 is 4 marks)

Mark scheme · P4D Pure: Sequences and Series (incl. Binomial Expansion): Fluency and Exam Drill

Question 1

B1 32 cao
Answer: 32

Question 2

B1 25 cao
Answer: 25

Question 3

B1 108 cao
Answer: 108

Question 4

B1 25 cao
Answer: 25

Question 5

B1 10 cao
Answer: 10

Question 6

B1 7 cao
Answer: 7

Question 7

B1 38 cao
Answer: 38

Question 8

B1 45 cao
Answer: 45

Question 9

B1 40 cao
Answer: 40

Question 10

B1 1 + 9x cao
Answer: 1 + 9x

Question 11

M1 uses u3 = a + 2d = 17
A1 a = 9 cao
Answer: a = 9

Question 12

M1 uses S_n = n(n+1)/2 (or the arithmetic series formula with a=1, d=1, n=20)
A1 210 cao
Answer: 210

Question 13

M1 uses 5C2 x 3²
A1 90 cao
Answer: 90

Question 14

M1 uses u20 = a + 19d = 84 to find d
A1 d = 4
A1 S20 = 920 (using the correct sum formula), cao
Answer: d = 4; S20 = 920

Question 15

M1 uses u4 = a r³ = 162
A1 r = 3
A1 u6 = 1458 cao
Answer: r = 3; u6 = 1458

Question 16

M1 identifies a = 7, d = 4
M1 correct use of S_n = n/2(2a+(n-1)d) with n = 15
A1 525 cao
Answer: 525

Question 17

M1 uses the correct general term 6C3 (2)³ x³
A1 correct evaluation 6C3=20, 2³=8
A1 160 cao
Answer: 160

Question 18

M1 identifies a = 150, d = 12, n = 24
M1 correct substitution into S_n = n/2(2a+(n-1)d)
A1 correct unsimplified value 12(300+276)
A1 6912 cao
Answer: 6912 units

Question 19

M1 uses S_infinity = a/(1-r) = 81
A1 r = 1/3
M1 correct use of S_n = a(1-rⁿ)/(1-r) with n = 5
A1 awrt 80.7
Answer: r = 1/3; S5 = 80.7 (3 s.f.)

Question 20

M1 sets consecutive differences equal: (2k+1) - (k-2) = (5k-4) - (2k+1)
M1 simplifies to a linear equation, k + 3 = 3k - 5
A1 k = 4 cao
A1 common difference = 7 (from terms 2, 9, 16), cao
Answer: k = 4; common difference = 7

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Pure: Sequences and Series (incl. Binomial Expansion): Fluency and Exam Drill - Worksheets, Questions and Revision

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P4D Pure: Sequences and Series (incl. Binomial Expansion): Fluency and Exam Drill

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