# A sculptor is using a pattern of glass cubes to create a sculpture with 5 sections. The first section has 4 cubes, the second section has 8 cubes, and the third section has 16 cubes. If the pattern continues, how many cubes will be in the fifth section?

Apr 2, 2018

$64$ glass cubes will be in $5$ th section.

#### Explanation:

The pattern is of geometric sequence whose first term is $a = 4$,

common ratio is $r = \frac{8}{4} = 2$ . In geometric sequence the $n$th

term is T_n=a*r^(n-1) ; n=5 :.T_5= 4*2^(5-1)= 4 *2^4=64

$64$ glass cubes will be in $5$ th section. [Ans]

Apr 2, 2018

color(green)(64 tiles

#### Explanation:

Number of cubes $\left(n\right)$ in the first section $= {2}^{2} = 4$ {here, $n = 1$}

Number of cubes $\left(n\right)$ in the second section $= {2}^{3} = 8$ {here, n=2}

Thus, we see that in each section, number of cubes $= {2}^{n + 1}$
So, number of cubes in the fifth section$= {2}^{5 + 1} = {2}^{6} = 64$