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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:

 

(iii) (a) If 2 more matchsticks are added in each figure, then will the number of matchsticks in each figure still form an AP If yes, find the number of matchsticks used in the 10th figure.
1 77  
2 74  
3 73  
4 70  

Ans.

(1)

If two more matchsticks are added to each figure, the new sequence is:
12 + 2, 19 + 2, 26 + 2, … i.e., 14, 21, 28, …

24-14=7=28-21

Hence, the sequence is an AP where a=14,??d=7 

We need to find a10: an=a+(n-1)da10=14+9×7=14+63=77

The number of matchsticks used in the 10th figure is 77