Grade 11 Geometric Progression HELP PLEASE

The first term in a geo. series is 3, last term is 48 and sum of the series is 93. Find r. (constant ratio)

we use the formulas ar^(n-1) = tn

and Sn = a ( r^n - 1)/(r-1)

Start with a = 3
The last term becomes, assuming there are "n" terms in the sequence, ar^(n-1) = 3r^(n-1) = 48
So r^(n-1) = 16 (dividing both sides by 3)
Using the laws of exponents, you can rewrite by saying (r^n) / r = 16
Multiply both sides by r to get
r^n = 16r

Sn = a(r^n - 1)/(r-1) = 3(r^n - 1)/(r-1) = 93
(r^n - 1)/(r-1) = 31

Substituting from above for r^n

(16r - 1)/(r - 1) = 31
16r - 1 = 31r - 31
-15r - 1 = -31
-15r = -30
r = 2 <-- ANSWER