Question

which term in progression,18,-12,8,.....is 512/729

Answer 1

Correction : Second Term is +12.
......................................…

18, 12, 8, 16/3, ...

This is a G.P. with a = 18

r = 12/18 = 2/3.

If the (n)th term is 512 / 729, then

a. r^(n-1) = 512/729

18. r^(n-1) = 512/729

r^(n-1) = 512 / ( 729 x 18 ) = 256 / (27². 3²) = ( 2^8)/(3^8) = (2/3)^8

(2/3)^(n-1) = (2/3)^8

n - 1 = 8

n = 9 .................. Ans.

Thus ( 9 )th term is 512/729.