Question

In the given figure, write down the expressions for the number of matchstick in the $n$^th shape.

Answer 1

Step 1: Data from given diagram

Consider the matchstick pattern in the given figure.

We can make first shape using $6$ matchsticks.

Now, for second shape, we need $11$ matchsticks.

Similarly, for third shape, we need $16$ matchsticks.

Step 2: Finding generalized formula

Number of shapes	Number of matchsticks	Observation and analysis of pattern	Generalization formula
$1$	$6$	$6+0$
$2$	$11$	$6+5=6+1\times 5=6+\left(2-1\right)\times 5$
$3$	$16$	$6+10=6+2\times 5=6+\left(3-1\right)\times 5$
:	:
:	:
$n$		Proceeding as above general pattern is $6+\left(n-1\right)\times 5$	$5n+1$

The number of matchsticks used for $n$^th shape = $5n+1$

Hence, the number of matchsticks used for $n$^th shape is $5n+1$.