Determine whether the sequence converges or diverges. if it converges, give the limit.

48, 8,4/3 ,2/9 ,

the sequence is geometric, with the common ratio being 1/6 (48 * 1/6 = 8

The formula for a geometric sequence is cr^n where "c" is a constant  and "r" is the common ratio 
=48(1/6)^n. 

A geometric series converges only if the absolute value of the common ratio is < It diverges if the ratio is >or equal to 1.
 the ratio is 1/6, so the sequence converges. 

Now in this case, the limit seems to approach 0,
 values can only keep getting smaller.
 If the limit approaches 0, then the series will converge to a definite sum
 S = c / (1 - are) 
S = 48 / (1 - 1/6) 
S = 57.6 

series converges, has a limit of 0,
 sum of 57.6.
hope this helps