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?

Question

1082 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-02T11:31:05

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

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

common ratio is #r=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]

Answer 2 · 2018-04-02T11:35:31

#color(green)(64# tiles

Number of cubes #(n)# in the first section #=2^2=4# {here, #n=1#}

Number of cubes #(n)# 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#