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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:

 

(i) Write the AP for the number of triangles used in the figures. Also, write the nth term of this AP.
1 an=2(n+1)  
2 an=1(n+2)  
3 an=1(2+2)  
4 an=3(n+2)  

Ans.

(1)

The AP formed by the number of triangles in each figure is: 4, 6, 8, …

Here, a=4,??d=6-4=8-6=2 

The nth term of an AP is an=a+(n-1)d⇒an=4+(n-1)×2=4+2n-2=2n+2=2(n+1)So, an=2(n+1)