Question

Match the figures to their corresponding algebraic representation (where n > 0).

• A. $n^2$
• B. $n+1$
• C. $2n-1$

Answer 1

$Case\left(i\right)$
The number of matchsticks follow the pattern $2,3,4,5$
which is in the pattern $n+1$. We can see it clearly:
$n=1,n+1=2$
$n=2,n+1=3n=3,n+1=4n=4,n+1=5$


$Case\left(ii\right)$:

Here, the pattern $1,4,9,16$ represents the number of squares in each figure. The numbers are perfect squares.

So, the correct algebraic representation is $n^2$ which can be checked by substituting the values of $n$ in $n^2$.

$n=1,n^2=1n=2,n^2=4n=3,n^2=9n=4,n^2=16$


$Case\left(iii\right)$

Here, the number of squares follow the pattern

$n=1,2n-1$$=2\times 1-1=2-1=1$
Similarly,
$n=2,2n-1=3n=3,2n-1=5n=4,2n-1=7$