Question

1. In each of the following patterns, construct next figure.
2. In each case, if n denotes the number of figure and F denotes the number of matchsticks used, find F in terms of n.
3. Also find, in each case, how many matches are required to make the: 16th figure and 30th figure.

1. 
2. 
3. 
4. 
5. 
6. 

Answer 1

a

.

b

.

c

.

d

e

f

.

i.
(a) F = 3n + 2
(b) F = 4n + 1
(c) F = 5n + 3
(d) F = 5n + 1
(e) F = 4n + 1
(f) F = 4n - 2

ii. 16^th figure
(a) F = 3 x 16 + 2 = 50
(b) F = 4 x 16 + 1 = 65
(c) F = 5 x 16 + 3 = 83
(d) F = 5 x 16 + 1 = 81
(e) F = 4 x 16 + 1 = 65
(f) F = 4 x 16 - 2 = 62

iii. 30^th figure
(a) F = 3 x 30 + 2 = 92
(b) F = 4 x 30 + 1 = 121
(c) F = 5 x 30 + 3 = 153
(d) F = 5 x 30 + 1 = 151
(e) F = 4 x 30 + 1 = 121
(f) F = 4 x 30 - 2 = 118