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Solution


Q.

In Mathematics, relations can be expressed in various ways. Matchstick patterns are an example of linear relations. Different strategies can be used to calculate the number of matchsticks used in different figures.

Based on the above information, answer the following questions:

 

(ii) Which figure has 61 matchsticks
1 8th figure  
2 7th figure  
3 5th figure  
4 4th figure  

Ans.

(1)

The AP formed by the number of matchsticks in the figure is:
12, 19, 26, …

Here, a=12, d=19-12=26-19=7

Let the nth figure have 61 matchsticks. Then:

an=6112+(n-1)7=61(n-1)7=49⇒n-1=7⇒n=8

The 8th figure has 61 matchsticks.