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Observe the following pattern of squares made with matchsticks. Neighbouring squares share a common matchstick, i.e., the squares are not separate. What is the general rule that predicts the number of matchsticks in terms of the number of squares? (The lines in the diagram represent matchsticks)

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3 x + 2

3 x + 1

4 x + 2

4 x + 1

answer is B.

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Detailed Solution

It is given diagrams,
Question Image

Carefully observe that after removing the vertical matchstick at the end of each pattern, a pattern of Cs is left.
Collecting the data we get,

Number of Squares	Number of Matchsticks	Pattern
1	4	3+1= (1×3) +1
2	7	6+1= (2×3) +1
3	10	9+1= (3×3) +1
4	13	12+1= (4×3) +1

We can observe that the pattern is = (Number of squares ×3) + 1
If we assume that the number of squares is ‘x’. Then, the pattern will be =

3 x + 1

Hence option (2) is correct.

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