Answer:
See the table below
For n, the answer is 2n+1
Step-by-step explanation:
The number of trees in each figure represents an arithmetic sequence where the difference between subsequent figures is 2 (caled the common difference)
So the sequence is
Figure(n) Number of Trees
1 3
2 5
3 7
4 9 (7+2)
5 11 (9+2)
n 2n + 1
In general, for any arithmetic sequence we can write an equation for the nth term as [tex]a_n = a_0 + d(n-1)[/tex] where [tex]a_0[/tex] is the first term and d is the common difference
So for this example, we have [tex]a_0 = 3[/tex] and d=2 giving
[tex]a_n = 3 + 2(n-1) = 3 + 2n -2 = 2n + 1[/tex]
This is
