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11+ · Number and Algebra

EP.M130 Sequences: Term-to-Term and Position-to-Term

GL ASSESSMENT GL-11PLUS-MATHS · Calculators not allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Find the next number in the sequence: 4, 9, 14, 19, ____

A) 20
B) 24
C) 23
D) 29
E) 22

(Total for Question 1 is 1 mark)

Describe the rule for the sequence: 12, 9, 6, 3, 0,...

(Total for Question 2 is 1 mark)

Continue this sequence: 3/2, 2, 5/2, 3, ____, ____

(Total for Question 3 is 2 marks)

The nth term of a sequence is a_n = 5n - 2. What is the 10th term?

A) 50
B) 48
C) 45
D) 52
E) 47

(Total for Question 4 is 1 mark)

Find the term-to-term rule for this sequence: 2, 6, 18, 54,...

(Total for Question 5 is 1 mark)

The nth term of a sequence is a_n = 3n² - n.

(a)Find a₄.(1)

(b)Find a₁₀.(1)

(Total for Question 6 is 2 marks)

The nth term of a sequence is a_n = 7n - 5. Find the 100th term.

(Total for Question 7 is 2 marks)

Which term of the sequence with nth term a_n = 2n + 1 has value 101?

(Total for Question 8 is 2 marks)

The sequence 1, 4, 9, 16,... is made from an nth-term rule. What is the 15th term?

A) 210
B) 225
C) 240
D) 256
E) 221

(Total for Question 9 is 1 mark)

The nth term of a sequence is a_n = 4 - 3n. Find a₅₀.

(Total for Question 10 is 2 marks)

The sequence is 10, 7, 11, 8, 12, 9,... Find the 8th term.

(Total for Question 11 is 2 marks)

The nth term of a sequence is a_n = 1/2 n² + 3/2 n. Find a₂₅.

(Total for Question 12 is 3 marks)

Mark scheme · EP.M130 Sequences: Term-to-Term and Position-to-Term

Question 1

B1 correct option B (24) cao
Answer: B) 24 (sequence increases by 5 each time: 19 + 5 = 24).

Question 2

B1 "subtract 3" or "decrease by 3 each time" cao
Answer: Subtract 3 each time.

Question 3

M1 identify the step change +1/2 (difference between consecutive terms) seen
A1 correct next two terms 7/2, 4 cao
Answer: 7/2, 4

Question 4

B1 correct option B (48) cao
Answer: B) 48

Question 5

B1 multiply by 3 each time ("times 3" or "multiply by 3") cao
Answer: Multiply by 3 each time.

Question 6

(a) B1 a₄ = 3(4²) - 4 = 48 - 4 = 44 cao
(a) Answer: 44
(b) B1 a₁₀ = 3(10²) - 10 = 300 - 10 = 290 cao
(b) Answer: 290

Question 7

M1 substitute n = 100 into 7n - 5 seen (7 x 100 - 5)
A1 695 cao
Answer: 695

Question 8

M1 attempt to solve 2n + 1 = 101 (2n = 100) seen
A1 n = 50 cao
Answer: 50

Question 9

B1 correct option B (225) cao
Answer: B) 225

Question 10

M1 substitute n = 50 to give 4 - 3 x 50 seen
A1 -146 cao
Answer: -146

Question 11

M1 identify alternating rule (-3, +4) or equivalent pattern seen
A1 8th term = 10 cao
Answer: 10

Question 12

M1 calculate n² for n = 25: 25² = 625 seen
M1 calculate 3n for n = 25: 3 x 25 = 75 and form (625 + 75) seen
A1 350 cao
Answer: 350

Sequences: Term-to-Term and Position-to-Term - Worksheets, Questions and Revision