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 pattern has 1 square. The second pattern has 4 squares, and so on.
So if we take any figure, the number of squares in the figure will be equal to the square of the order of the figure.
If we take the $n^{th}$ figure, we will have $n^2$ squares in that figure.
Hence, the next figure, i.e., $5^{th}$ figure will have $5^2=25$ squares.