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?

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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#