Question 14 Marks

i. In each of the following patterns, construct next figure.
ii. In each case, if $n$ denotes the number of figure and $F$ denotes the number of matchsticks used, find $F$ in terms of $n$.
iii. Also find, in each case, how many matches are required to make the: $16$ th figure and 30th figure.
a.
b.
c.
d.

e.
f.

Answer

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

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