Ineed on these other 2 sequences.

bear in mind that one can always get the common ratio by simply dividing any of the terms by the one before it namely, say 18÷12 or 27÷18.

591.09375

1/4

Step-by-step explanation:

"Find the sum of the first 8 terms of the geometric sequence that begins: 12, 18, 27,..."

The sum of the first n terms of a geometric sequence is:

S = a (1 − r^n) / (1 − r)

where a is the first term and r is the common ratio.

Here, the first term is 12, so a = 12.  The common ratio is 18/12 = 1.5.  So the sum of the first 8 terms is:

S = 12 (1 − 1.5^8) / (1 − 1.5)

S = 591.09375

"Find the sum of the infinite geometric sequence that begins 1/12, 1/18, 1/27,..."

The sum of an infinite geometric sequence is:

S = a / (1 − r)

Here, the first term is 1/12, so a = 1/12.  The common ratio is (1/18) / (1/12) = 2/3.  So the infinite sum is:

S = 1/12 / (1 − 2/3)

S = 1/4

905.22 cubic