IGCSEFM-Sequences-Worksheet

```IGCSE Further Maths Sequences
Exercise 1
1. [Worksheet Q1] A linear sequence
starts
250 246 242 238
Which term is the first to have a
negative value?
2. [AQA Worksheet] A sequence has πth
term
5π+2
.
2π
Show that the limiting
value of the sequence S, as π → ∞ is
2.5
3. [Set 1 Paper 2 Q3]
(a) The πth term of a sequence is
4π − 10.
(a)(i) Show that the (π + 1)th term
can be written as 4π − 6.
(a)(ii) Prove that the sum of any two
consecutive terms of the sequence is
divisible by 8.
(b) The πth term of a different
3π
sequence is π+5
(b)(i) Explain why 1 is not a term in
this sequence.
(b)(ii) Work out the limiting value of
the sequence as π → ∞.
4. [Set 2 Paper 1 Q2] Here is a linear
sequence:
4 11 18 25 …
(a) Work out an expression for the
πth term.
(b) How many terms are less than
150?
5. [Set 2 Paper 2 Q11]
The πth term of sequence X is ππ + π.
The πth term of sequence Y is ππ + π.
(a) Show that the sequences have the
same first term.
(b) The 2nd term of sequence X is
equal to the 3rd term of sequence Y.
Show that π = 2π.
(c) Prove that:
ππ‘β π‘πππ ππ π πππ’ππππ π 2π + 1
=
ππ‘β π‘πππ ππ π πππ’ππππ π
π+2
6. [Set 4 Paper 2 Q11]
(a) π(π) = π2 + π Show that
π(π + 1) − π(π) = 2π + 2
(b) The πth term of a sequence is
π2 + π
Two consecutive terms in the
sequence have a difference of 32.
Work out the two terms.
7. [June 2012 Paper 1 Q10] The πth
term of the linear sequence 2, 7, 12,
17, … is 5π − 3. A new sequence is
formed by squaring each term of the
linear sequence and adding 1. Prove
algebraically that all the terms in the
new sequence are multiples of 5.
8. [Worksheet Q4]
(a) Write down the πth term of the
linear sequence
4 7 10 13 …
(b) Hence, write down the πth term of
16 49 100 169 …
(c) For the sequence in (b), show that
the 30th term is equal to the product
of the 2nd and 4th.
9. [AQA Worksheet]
This pattern of rectangles continues.
Show that the sequence of numbers
formed by the areas of these
rectangles has πth term.
π2 + 5π + 6
10. A linear sequence starts
π + π π + 3π π + 5π π + 7π
The 5th and 8th terms have values 35
and 59.
(a) Work out π and π.
(b) Work out the πth term of the
sequence.
11. [AQA Worksheet] A sequence has nth
term
3π+1
.
π
(a) Show that the difference between
the πth and (π + 1)th term is
1
π(π+1)
(b) Which are the first two
consecutive terms with a difference
less than 0.01?
(c) Write down the limiting value of
the sequence as π → ∞.
```