What is the sum of the geometric series in which a 1 = 7 , r = 3 and a n = 1701?

We need to find how many terms we have, as follows

1701  = 7(3)^n-1     divide both sides by 7

243 = 3^n-1   and 3⁵  = 243   so n = 6

So we have

S_n = a₁ [ (1-rⁿ) / (1 - r) ]

S₆ = 7 [ (1 - 3⁶) / (1 - 3) ]  =  7 [ 1 - 729] [ 1 - 3]  =  7 [-728] / [-2]  = 2548