Question

Find the pattern followed in figures given below and number of matchsticks to be used in the ${47}^{th}$ figure$.$

Answer 1

In the given figure count the number of matchsticks for the patterns

In first pattern the number of matchsticks $=4$

$=3\times 1+1$

In second pattern the number of matchsticks $=10$

$=3\times 3+1$

In third pattern the number of matchsticks $=16$

$=3\times 5+1$

In fourth pattern the number of matchsticks $=22$

$=3\times 7+1$

In $n^{th}$ pattern the number of matchsticks $=3\times \left(2n-1\right)+1$

In ${47}^{th}$ pattern the number of matchsticks $=3\times \left(2\times 47-1\right)+1$

$=3\times 93+1$

$=279+1$

$=280$

Hence, the number of matchsticks in ${47}^{th}$ pattern are $280$