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How do you write the expression for the nth term of the geometric sequence #a_1=16, a_4=27/4, n=3#?

1 Answer

Feb 23, 2018

#n# th term is #a_1*r^(n-1)# and #a_3=16#

Explanation:

In Geometric progression #n# th term is #a_1*r^(n-1)# where

#a_1# is first term and #r# is the common ratio.

#a_1=16 , a_4=27/4#

#:. a_4=16*r^(4-1) or a_4= 16r^3 = 27/4 or r^3= 27/64#or

#r= root(3)(27/64)=3/4#. When #n=3 :. a_3= 16* (3/4)^(3-1)#

or # a_3= 16* (3/4)^(3-1)=16*(3/4)^2=9#

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