A geometric sequence is 3/4,9,108,1296,15,552,186,624 ... which is the general term of the sequence?

a (n) = (3/4) (12) ^ (n-1)

Step-by-step explanation:

The general term of a geometric sequence is a (n) = a (1) (r) ^ (n-1), where a (1) is the first term, r is the common factor and n is the index (first, second, third, etc.).

Here the first term is 3/4. By what figure must we multiply 3/4 to obtain the next term, 9? Dividing 9 by 3/4 results in 12. The next term, 108, is found by multiplying 9 by 12. And so on. Thus, we conclude that the common factor, r is 12.

Thus, the general formula becomes:

a (n) = (3/4) (12) ^ (n-1).