geometric sequence question?

The geometric progression should be :
2√3, 12, 24√3, 144, 288√3.......

First term, a = 2√3
common reatio, r = 12/2√3 = 24√3/12 = 144/24√3 = 288√3/144 = 2√3

The 10th term
= a r^9
= (2√3) × (2√3)^9
= (2√3)^10
= 2^10 × (√3)^10
= 1024 × [3^(1/2)]^10
= 1024 × 3^5
= 1024 × 243
= 248832

The answer: d) 248832

(Oops! 24√3 , not 23√3)
Yes, you have the ratio correctly.
It should be no trouble to find the 10th term -- 9 terms froward from the first.
t_10 = t_1 * r^9
= 2√3 * (2√3)^9
= (2√3)^10 . . . . . . . = 12^5, if you prefer
= 2^10 * 3^5
= 1024 * 243
= 128832

2√3, 12, 24√3, 144, 288√3....
an = 2^n 3^(n/2)
10th term is = 248832.
Answer choice:
d) 248832