Question

Given below is a pattern made using squares. Observe the pattern and tell the number of squares in the next figure in the sequence. Also find the general form which represents the number of squares in the sequence.

• A. The pattern doesn’t follow with the next set of squares
• B. $16,n^2$
• C. $25,2n+1$
• D. $25,n^2$

Answer 1

The correct option is D $25,n^2$

The figures have 1, 4, 9 and 16 squares respectively. The first figure has 1 square. The second figure has 4 squares, and so on.

Hence, if we take the $n^{th}$ figure, we have $n^2$ squares in that figure.

Hence, the next figure, i.e. $5^{th}$ figure will have $5^2=25$ squares.