Question

Which Term Of the following Sequences root 3,3,3root3,.....is 729 wq

Answer 1

Hi ,

√3 , 3 , 3√3 , .... 729

Here ,

first term = a = √3

a2 = 3

a3 = 3√3

a2 / a1 = 3/√3 = √3

a3 / a2 = 3√3 / 3 = √3

Therefore ,

a2 / a1 = a3 / a2 = √3 = r ( common ratio )

given sequence is in Geometric progression

n th term = an = 729

ar^n-1 = 729

√3 × √3^n-1 = 3^6

3^[ 1/2 +( n - 1 )/2 ] = 3^6

1/2 + ( n - 1 ) / 2 = 6

( if a^m = a ^n then m = n )

( 1 + n - 1 ) / 2 = 6

n = 2 × 6

n = 12

Therefore ,

12th term of the sequence is 729

I hope this helps you.

:)