SOLUTION: Find the 8th term in the geometric sequence with t4 = 48 and t6 = 192.

Algebra ->  Sequences-and-series -> SOLUTION: Find the 8th term in the geometric sequence with t4 = 48 and t6 = 192.      Log On


   

Question 398942: Find the 8th term in the geometric sequence with t4 = 48 and t6 = 192.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Geometric sequence:

a%5Bn%5D+=+a%5B1%5D%2Ar%5E%28n-1%29

Question states:

a%5B4%5D+=+a%5B1%5D%2Ar%5E3+=+48 OR a%5B1%5D+=+48%2Fr%5E3

a%5B6%5D+=+a%5B1%5D%2Ar%5E5+=+192

a%5B6%5D+=+48%2Fr%5E3%2Ar%5E5+=+192

              r^2 = 4  

    r = 2   a%5B1%5D = 48/8 = 6 , if r = -2, then first term would be -6

irregardless:

a%5B8%5D+=+6%2A2%5E7+=+-6%2A%28-2%29%5E7+=+768+