If from each figure 5 matchsticks are removed, then will the number

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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) (b) If from each figure 5 matchsticks are removed, then will the number of matchsticks in each figure still form an AP If yes, find which figure will have 91 matchsticks.

1 13th figure

2 14th figure

3 12th figure

4 11th figure

Ans.
(1)

If 5 matchsticks are removed from each figure, the new sequence formed is:
12 – 5, 19 – 5, 26 – 5, … i.e., 7, 14, 21, …

$14 - 7 = 7, 21 - 14 = 7$

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

Let the nth figure have 91 matchsticks:

$a_{n} = 91 7 + (n - 1) 7 = 91 (n - 1) 7 = 84 \Rightarrow n - 1 = 12 \Rightarrow n = 13$

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