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Jlenok [28]
3 years ago
7

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?
Mathematics
1 answer:
posledela3 years ago
7 0

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}

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