Question

In the figure (c) , write down the expression for the number of matchsticks in the $n^{th}$ shape.

Answer 1

Forming the algebraic expression :

We can determine a pattern from the image to find the number of matchsticks required for making a fixed number of this shape.

From the image, we can see the after the first shape (which need $3$ matchsticks) we need only $2$ matchsticks to make another shape of same type.

So, for making $2$ shapes,

We need: $3+2\times 1=3+2=5matchsticks.$

Therefore, we need $5matchsticks$ for making $2$ shapes

So, for making $3$ shapes,

We need: $3+2\times 2=3+4=7matchsticks$

Therefore, we need $7matchsticks$ for making $3$ shapes

So, for making $4$ shapes,

We need: $3+2\times 3=3+6=9matchsticks$

Therefore, we need $9matchsticks$ for making $4$ shapes

So, for making $5$ shapes,

We need: $3+2\times 4=3+8=11matchsticks$

Therefore, we need $11matchsticks$ for making $5$ shapes

Therefore, for making $n^{th}$ shape we need $3+2\times \left(n-1\right)matchticks$ where, $n=Numberofshapes$