Question

A. What is the common ratio of the pattern?B. Write the explicit formula for the pattern?C. If the pattern continued how many stars would be in the 11th set?

Answer 1

Given:

The sequence of number of stars is 2,4,8,16

a) To find the common ratio of the pattern.

`\begin{gathered} \text{Common ratio=}\frac{2nd\text{ term}}{1st\text{ term}} \\ r=(4)/(2) \\ r=2 \end{gathered}`

Hence the common ratio is 2.

b) To find the explicit formula for the pattern.

The general for a geometric progression sequence is,

`a_n=a_1(r)^(n-1)_{}_{}`

Hence, the formula for the above pattern will be,

`a_n=2(2)^(n-1)`

c) To find the number of stars in 11th set.

Substitute n=11 in the explicit formula of the pattern.

`\begin{gathered} a_(11)=2(2)^(11-1) \\ a_(11)=2(2)^(10) \\ a_(11)=2(1024) \\ a_(11)=2048 \end{gathered}`

Hence, the number of stars in 11th set will be 2048.