Questions
Q1.
A polygon has n sides, where n > 5
When arranged in order of size, starting with the largest number, the sizes of the interior angles of the
polygon, in degrees, are the terms of an arithmetic sequence.
Here are the first five terms of this sequence.
177 175 173 171 169
Find the value of n
Show clear algebraic working.
n = ...........................................................
(Total for question = 6 marks)
Q2.
(2x + 23), (8x + 2) and (20x – 52) are three consecutive terms of an arithmetic sequence.
Prove that the common difference of the sequence is 12
(Total for question = 4 marks)
Q3.
Here are the first five terms of an arithmetic sequence.
8 15 22 29 36
Work out the sum of all the terms from the 50th term to the 100th term inclusive.
...........................................................
(Total for question = 4 marks)
Q4.
An arithmetic series has first term 1 and common difference 4
Find the sum of all terms of the series from the 41st term to the 100th term inclusive.
...........................................................
(Total for question = 4 marks)
Q5.
The sum of the first N terms of an arithmetic series, S, is 292
The 2nd term of S is 8.5
The 5th term of S is 13
Find the value of N.
Show clear algebraic working.
N = ...........................................................
(Total for question = 5 marks)
Q6.
Here are the first five terms of an arithmetic sequence.
1 5 9 13 17
(a) Find an expression, in terms of n, for the nth term of this sequence.
...........................................................
(2)
The nth term of another arithmetic sequence is 3n + 5
(b) Find an expression, in terms of m, for the (2m)th term of this sequence.
...........................................................
(1)
(Total for question = 3 marks)
Q7.
(a) Factorise 5a − 3a2
...........................................................
(2)
(b) Expand
(i) 2(4 − 3w)
...........................................................
(ii) y2 (y + 10)
...........................................................
(3)
(c) W =
a = 1.28 b = 0.8
Work out the value of W.
W = ...........................................................
(2)
(Total for question is 7 marks)
Q8.
The first four terms of an arithmetic sequence are
5 9 13 17
(a) Write down an expression, in terms of n, for the nth term.
...........................................................
(2)
(b) Write down an expression, in terms of n, for the (n + 1)th term.
...........................................................
(1)
(Total for question = 3 marks)
Q9.
Here are the first five terms of a number sequence.
7 11 15 19 23
(a) Find an expression, in terms of n, for the nth term of this sequence.
...........................................................
(2)
The nth term of a different number sequence is given by 80 – 2n
(b) Write down the first 3 terms of this sequence.
................ , ................ , ................
(2)
Yuen says there are no numbers that are in both of the sequences.
Yuen is correct.
(c) Explain why.
.............................................................................................................................................
.............................................................................................................................................
(1)
(Total for question = 5 marks)
Q10.
Here is a sequence of patterns made from centimetre squares.
(a) Find an expression, in terms of n, for the total number of centimetre squares in Pattern number n.
...........................................................
(2)
A pattern in this sequence has 88 centimetre squares.
(b) Work out the Pattern number of this pattern.
...........................................................
(2)
(Total for Question is 4 marks)
Q11.
Here are the first five terms of an arithmetic sequence.
7 10 13 16 19
Find an expression for the nth term of the sequence.
...........................................................
(Total for question = 2 marks)
Q12.
Here are some rows of a number pattern.
(a) Write down the Row number of the row that has 676 in Column 2
...........................................................
(1)
(b) For Row number n,
(i) write down an expression, in terms of n, that should go in Column 1
...........................................................
(ii) write down an expression, in terms of n, that should go in Column 3
...........................................................
(2)
(Total for question = 3 marks)
Q13.
The 3rd term of an arithmetic series, A, is 19
The sum of the first 10 terms of A is 290
Find the 10th term of A.
...........................................................
(Total for question = 5 marks)
Q14.
The first term of an arithmetic series is (2t + 1) where t > 0
The nth term of this arithmetic series is (14t – 5)
The common difference of the series is 3
The sum of the first n terms of the series can be written as p(qt – 1)r where p, q and r are integers.
Find the value of p, the value of q and the value of r
Show clear algebraic working.
p = ................................................. q = .................................................r = .................................................
(Total for question = 4 marks)
Q15.
Here are the first 4 terms of an arithmetic sequence.
85 79 73 67
Find an expression, in terms of n, for the nth term of the sequence.
...........................................................
(Total for question = 2 marks)
Q16.
Here are the first five terms of an arithmetic sequence.
7 11 15 19 23
Write down an expression, in terms of n, for the nth term of this sequence.
(Total for question = 2 marks)
Q17.
Here are the first five terms of an arithmetic sequence.
Find the sum of the first 100 terms of this sequence.
...........................................................
(Total for question = 2 marks)
Q18.
An arithmetic sequence has first term 8 and common difference 11
The sequence has k terms, where k > 21
The sum of the last 20 terms of the sequence is 10 170
Find the value of k
Show clear algebraic working.
k = ...........................................................
(Total for question = 5 marks)
Q19.
An arithmetic series has first term a and common difference d.
The sum of the first 2n terms of the series is four times the sum of the first n terms of the series.
Find an expression for a in terms of d.
Show your working clearly.
a = ...........................................................
(Total for question = 4 marks)
Q20.
Here are the first four terms of an arithmetic sequence.
38, 31, 24, 17
Find an expression, in terms of n, for the nth term of the sequence.
...........................................................
(Total for question = 2 marks)
Q21.
Here are the first three terms of an arithmetic sequence.
8p, 7p − 3, 4p + 2
The sum of the first n terms of the sequence is −1914
Work out the value of n
Show your working clearly.
n = ...........................................................
(Total for question = 5 marks)
Q22.
The sum of the first 80 terms of an arithmetic series, S, is 470
The 75th term of S is 14.5
The sum of the first X terms of S is 171
Work out the value of X
Show your working clearly.
X = ...........................................................
(Total for question = 6 marks)
Q23.
In a warehouse there are two types of shelves, type R and type S.
These two types of shelves are arranged into shelving units that form a sequence of patterns.
Here are the first three terms in the sequence.
The width of each type R shelf is 2.4 m and the width of each type S shelf is 3.5 m
(a) Work out the total width of a shelving unit that has 6 type R shelves.
........................................................... m
(2)
A shelving unit has n type R shelves.
The total width of this shelving unit is W metres.
(b) Find an expression for W in terms of n
Give your answer in its simplest form.
W = ...........................................................
(2)
(Total for question = 4 marks)
Q24.
Here are the first four terms of an arithmetic series.
Given that the 15th term of the series is (90 + 2k),
calculate the sum of the first 30 terms of the series.
...........................................................
(Total for question = 5 marks)
Q25.
An arithmetic series has first term a and common difference d, where d is a prime number.
The sum of the first n terms of the series is Sn and
Sm = 39
S2m = 320
Find the value of d and the value of m
Show clear algebraic working.
d = ...........................................................
m = ...........................................................
(Total for question = 5 marks)
Q26.
The sum of the first 10 terms of an arithmetic series is 4 times the sum of the first 5 terms of the same
series.
The 8th term of this series is 45
Find the first term of this series.
Show clear algebraic working.
...........................................................
(Total for question = 5 marks)
Mark Scheme
Q1.
Q2.
Q3.
Q4.
Q5.
Q6.
Q7.
Q8.
The correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct
method.
Q9.
Q10.
Q11.
Q12.
Q13.
Q14.
Q15.
Q16.
Q17.
Q18.
Q19.
Q20.
Q21.
Q22.
Q23.
Q24.
Q25.
Q26.
