Question

Which term of the gp 18,-12,8....is 512/729?

Answer 1

Let the first term be 'a'

The common difference be 'r'

nth term is = a*r^(n-1)

So

first term
a1 = a*r^0
a = 18

second term 
a2 = a*r^1 = -12
hence r = -2/3

Third term 
a3 = 18*(-2/3)^2
     = 8
Hence 
a = 18
r = -2/3

512/729 = 18*(-2/3)^n  -------(1)
after cross multiplying 18 we have to find the power of n which satisfies (-2/3)^n = 256/6561

we obtain (-2)^8 = 256 and 3^8 = 6561

therefore (1) becomes
18*(-2/3)^8 = 512/729

n-1 = 8
Therefore it is the 9th term

Answer 2

Answer:

n=9

Step-by-step explanation:

a=18

r=-12/18

=-2/3

an=512/729

ar