Question 1067945
your conjecture is correct, but that doesn't tell you how many squares are in the nth sketch.


you can make a list as follows:


<pre>

sketch number        number of squares           formula

1                   3                            2 * 1 + 1
2                   5                            2 * 2 + 1
3                   7                            2 * 3 + 1
4                   9                            2 * 4 + 1
5                   11                           2 * 5 + 1
6                   13                           2 * 6 + 1
.
.
.
n                   2 * n + 1

</pre>


your next number of squares will always be 1 more than 2 times the sketch number.