Question

Match the following figures according to the number of matchsticks required to make $n^{th}$ figure.

• A. 5n+1
• B. 2n+1
• C. 4n+1

Answer 1

For $1^{st}$ row:
for $1^{st}$ figure, matchsticks required are
3 = 2$\times$1 + 1
for $2^{nd}$ figure, matchsticks required are
5 = 2$\times$2 + 1
for $3^{rd}$ figure, matchsticks required are
7 = 2$\times$3 + 1
hence for $n^{th}$ figure, matchsticks required are ​​​​​​​
2$\times$n + 1 = 2n+1

Similarly, for $2^{nd}$ row:
for $1^{st}$ figure, matchsticks required are ​​​​​​​
6 = 5$\times$1 + 1
hence for $n^{th}$ figure, matchsticks required are ​​​​​​​
5$\times$n + 1 = 5n+1

Similarly, for $3^{rd}$ row:
for $1^{st}$ figure, matchsticks required are ​​​​​​​
5 = 4$\times$1 + 1
hence for $n^{th}$ figure, matchsticks required are ​​​​​​​
4$\times$n + 1 = 4n+1