Answer:
Explicit formula: [tex]s_{n}=6(2)^{n-1}[/tex]
Step-by-step explanation:
Let the number of squares in [tex]n^{th}[/tex] layer be [tex]s_{n}[/tex]
Given:
Number of squares in first layer, [tex]s_{1}=6[/tex]
Number of squares in second layer, [tex]s_{2}=12[/tex]
Therefore, the number of squares increases by a factor of 2.
So, it follows a geometric sequence with the first term as 6 and common ratio of 2.
For a geometric sequence, the [tex]n^{th}[/tex] term with common ratio [tex]r[/tex] is given as:
[tex]s_{n}=s_{1}\times r^{n-1}[/tex]
Here, [tex]r=2,s_{1}=6[/tex]
∴ Explicit formula: [tex]s_{n}=6(2)^{n-1}[/tex]
