For geometric sequence, the general formula is:
An = A₀rⁿ⁻¹
So for n=3 and An = 13
13 = A₀r²
A₀ = 13/r² --> eqn 1
For n=7 and An = 208
208 = A₀r⁶ --> eqn 2
Solving simultaneously,
208 = (13/r²)(r⁶)
208 = 13r⁴
r = ⁴√208/13 = 2
Then, A₀ = 13/2² = 13/4
1. The general formula would then be: An = (13/4)(2)ⁿ⁻¹
2. If n=19,
An = (13/4)(2¹⁸) = 851,968
