Question

In each of the following patterns,

(i) In each case, if n denotes the nth number of figure in each case and F denotes the number of matchsticks used, find F in terms of n.

(ii) Also find, in each case, how many matchsticks are required to make the:
16th figure and 30th figure.

(a)

(b)

(c)

(d)

(e)
(f)
$\left[3\right]$

Answer 1

(i) (a) $F=3n+2$
(b) $F=4n+1$
(c) $F=5n+3$
(d) $F=5n+1$
(e) $F=4n+1$
(f) $F=4n–2$
$\left[1\right]$
16th figure
(a) $3\times 16+2=48+2=50$
(b) $F=4\times 16+1=64+1=65$
(c) $F=5\times 16+3=80+3=83$
(d) $F=5\times 16+1=80+1=81$
(e) $F=4\times 16+1=64+1=65$
(f) $F=4\times 16–2=64–2=62$
$\left[1\right]$

30th figure
(a) $F=3\times 30+2=90+2=92$
(b) $F=4\times 30+1=120+1=121$
(c) $F=5\times 30+3=150+3=153$
(d) $F=5\times 30+1=150+1=151$
(e) $F=4\times 30+1=120+1=121$
(f) $F=4\times 30–2=120–2=118$
$\left[1\right]$