Identify the 19th term of a geometric sequence where a1 = 14 and a9 = 358.80. round the common ratio and 19th term to the nearest hundredth.

An = ar^(n-1) 

where, an = nth term, n=number of terms, r=common ratio 
a = first term 

given: a =14, a9= 358.80, n = 9, r=? 

an = ar^(n-1) 
358.80 = (14)*(r)^(9-1) 
358.80 = 14*(r^8) 
r^8 = 358.80/14 
r^8 = 25.63 
r = 1.5 .. . .commonratio 

solve for 19th term... 
a19=? , n = 19, r = 1.5, a=14 
an = ar^(n-1) 
a19 = (14)*(1.5)^(18) 
a19=14*(1477.89) 
a19 = 20 690.49 . . .ans. 

hence, 19th term is 20 690.49