Question #42911

1 Answer
Jul 10, 2016

Answer:

#T_12 = 1/1024 , " " T_15 = 1/8192," "T_20 = 1/262144#

Explanation:

This is a geometric sequence.

Each term is half of the preceding term, so the
common ratio, "r" = #1/2#

The First term, "a" = 2.

The sequence can therefore be defined by its general term:

#T_n = ar^(n-1) " "rArr 2 xx (1/2)^(n-1)#

This will simplify to #T_n = (1/2)^(n-2)#

#T_12 = (1/2)^10= 1/1024#

#T_15 = (1/2)^13= 1/8192#

#T_20 = (1/2)^18= 1/262144#