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

2 Answers
Mar 27, 2018

18.96

Explanation:

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

Mar 27, 2018

t_10=512/27

Explanation:

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.....towhere 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