Question

A group of students is arranging squares into layers to create a project. The first layer has 6 squares. The second layer has 12 squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?

Answer 1

Answer:

Explicit formula: $s_{n}=6(2)^{n-1}$

Step-by-step explanation:

Let the number of squares in $n^{th}$ layer be $s_{n}$

Given:

Number of squares in first layer, $s_{1}=6$

Number of squares in second layer, $s_{2}=12$

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 $n^{th}$ term with common ratio $r$ is given as:

$s_{n}=s_{1}\times r^{n-1}$

Here, $r=2,s_{1}=6$

∴ Explicit formula: $s_{n}=6(2)^{n-1}$