Question

which term of the G.P.3,-3√3,9,-9√3,....is 729?

Answer 1

Hi ,

3 , -3√3 , 9 , .... , 729 are in G. P

First term = a = 3 ,

Common ratio ( r ) = a2/a1

r = ( - 3√3 ) /3

r = - √3

nth term = 729

ar^n-1 = 729

3 × ( - √3 )^n -1 = 729

( - √3 ) ^n-1 = 729/3

= 243

( - √3 )^n / ( - √3 ) = 243

( - √3 ) ^n = ( - √3 ) × 3^5

( - √3 )^n = ( - √3 ) × ( - √3 ) ^10

( - √3 ) ^n = ( - √3 ) ^ 11

[ Since if a^m = a^n then m = n ]

n = 11

Therefore ,

11th term in given G. P = 729

I hope this helps you.

:)