If 3rd term of a g p is 324 and 7th term is 64, then find 10th term?

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Answer 1 · 2018-03-27T15:02:51

#18.96#

The general term of the #n^(th)# term of a GP is #A*D^(n-1)#

Where A is the first term and D is the common ratio

3rd term is 324 so, #A*D^2=324#
7th term is 64 so, #A*D^6=64#

Solving these two equations, we get #D=2/3# and #A=729#

So now, 10th term is #A*D^9=729*(2/3)^9#

#=18.96#

Answer 2 · 2018-03-27T15:46:11

#t_10=512/27#

Here,

3rd term =#t_3=324# and 7th term #= t_7=64.#

We have to find 10th term = #t_10#.

The nth term #t_n# of the G.P. with first term #a# and
common ratio #r# is

#color(red)(t_n=a*r^(n-1)#

So,

#t_3=ar^(3-1)=ar^2=324.....to(1)#

#t_7=ar^(7-1)=ar^6=64.....to(2)#

#=>ar^2*r^4=64.....to#where #ar^2=324#

#=>324r^4=64#

#=>r^4=64/324=16/81=(2/3)^4#

#=>r=2/3#

Hence,

#t_10=ar^(10-1)=ar^9=ar^6*r^3,....#where, #ar^6=64#

#=(64) (2/3)^3=64xx8/27#

#t_10=512/27#