Sequences

151.
Consider the sequence: 7,12,17,22,27,...
(a) Write the next 2 terms of the sequence.
.........................
(b) Write the nth term of the sequence.
.........................
(c) Given that the kth term is 212, find the value of k.
.........................
Paper 1
152.
Given the sequence: 12, 16, -16, -12,...
(a) Write down the next two terms of the sequence.
.........................
(b) Write an expression for the nth term.
.........................
Paper 1
153.
The columns n, P, Q and S show 4 sequences.

n P Q S 1 10 5 15 2 16 8 24 3 22 11 33 4


(a) Fill in the 3 missing numbers in the 4th row.
(b) Write a formula connecting
    (i) P,Q and S,
    (ii) n and Q.
(a) ......................... [0] (b) (i) ........................ [0]      (ii) ........................ [1]
Paper 1
94.
The diagram shows patterns formed using rods.
Pattern 1 Pattern 2 Pattern 3 Pattern 4

(a) Draw pattern 4.
See diagram [1]
(b) The table shows the number of rods used and triangle vertices formed in each pattern.
Pattern number 1 2 3 4 5 n
Number of rods 5 8 11 ... 17 38 p
Number of triangle vertices 3 6 ... 12 15 36 q
Complete structure 8 ... 20 ... 32 r
Complete the table.
......................... [2]
(c) Find the number of rods in pattern 20.
......................... [2]
(d) Write an expression for r, in terms of p and q.
r = ......................... [1]
Paper 3
96.
The diagram shows patterns with dotted and plain tiles.
pattern 1 pattern 2 pattern 3 pattern 4

(a) Complete the 4th pattern.
See diagram [1]
(b) Complete the table below.
Pattern number 1 2 3 4 5
Dotted tiles 1 3 5 ... ...
Plain tiles 3 6 11 ... ...
......................... [2]
(c) Write an expression, in terms of n, for the number of dotted tiles in the nth pattern.
......................... [2]
(d) Find the number of dotted tiles in the 20th pattern.
......................... [1]
(e) How many more dotted tiles are in pattern n + 7 than in pattern n?
......................... [1]
(f) Write an expression, in terms of n, for the number of plain tiles in the nth pattern.
......................... [2]
(g) Find the pattern with 227 plain tiles.
......................... [2]
Paper 3
97.
The diagrams show patterns with shaded and unshaded squares. The squares form a sequence.
Pattern 1 Pattern 2 Pattern 3 Pattern 4

(a) Complete pattern 4 to continue the pattern.
See diagram [2]
(b) Write the number of shaded squares in pattern 7.
......................... [2]
(c) The total number of squares in pattern 45 is 2116. Find the number of unshaded squares in pattern 45.
......................... [3]
(d) Find an expression, in terms of n, for the number of unshaded squares in pattern n.
......................... [3]
Paper 3
98.
The patterns show grey and white tiles.
pattern number 1 pattern number 2 pattern number 3 pattern number 4

(a) Draw the 4th pattern in the space above.
See diagram [1]
(b) State the name of the shape of tiles used in the pattern.
......................... [1]
(c) Complete the table.
Pattern 1 2 3 4 5
Number of grey tiles 2 3 4 ... ...
Number of white tiles 2 4 6 ... ...
......................... [2]
(d) Find the total number of tiles in the 20th pattern.
......................... [2]
(e) Write an expression, in terms of n, for the number of grey tiles in the nth pattern.
......................... [2]
Paper 3
100.
32, 25, 18, 11, 4, ...
These are the first 5 terms of a sequence.
Find:
(a) The 6th term,
......................... [1]
(b) The nth term,
......................... [2]
(c) Which term is equal to −332.
......................... [2]
Paper 3