To find the next number in the given sequence, let's analyze the pattern:
12, 12, 18, 45, 180, 1170, ___
Looking at the sequence, we can see that each number is obtained by multiplying the previous number by a certain factor.
The first number, 12, is multiplied by 1 to give the second number, 12.
The second number, 12, is then multiplied by 1.5 to give the third number, 18.
The third number, 18, is multiplied by 2.5 to give the fourth number, 45.
The fourth number, 45, is multiplied by 4 to give the fifth number, 180.
The fifth number, 180, is multiplied by 6.5 to give the sixth number, 1170.
Therefore, to find the next number, we need to multiply the sixth number, 1170, by 9.5.
1170 * 9.5 = 11085
So, the next number in the sequence is 11085.
Comparing this with the options provided:
A) 12285 - This option is close to the result we obtained, 11085.
B) 13540 - This option is not consistent with the pattern we observed.
C) 12380 - This option is not consistent with the pattern we observed.
D) 12543 - This option is not consistent with the pattern we observed.
Therefore, the correct answer is A) 12285.