Question

In the figure (b) , write down the expression for the number of matchsticks in the nth shape.

Answer 1

Explanation:- 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 1st shape (which need 6 matchsticks) we need only 5 matchsticks to make another shape of same type.

So, for making 2 shapes,

we need: $6+5\times 1=6+5=11matchsticks.$

Therefore, we need $11matchsticks$ for making 2 Shapes

So, for making 3 shapes,

we need: $6+5\times 2=6+10=16matchsticks$

Therefore, we need $16matchsticks$ for making 3 Shapes

So, for making 4 shapes,

we need: $6+5\times 3=6+15=21matchsticks$

Therefore, we need $21matchsticks$ for making 4 Shapes

Therefore, for making nth shape we need:-

$6+5\times \left(n-1\right)matchticks$

where, n= no of shapes