Is the following the sum of an arithmetic sequence a geometr

Is the following the sum of an arithmetic sequence, a geometric sequence, or neither, and what is the sum? sigma_k = 1^4 (7/5)^k sum of geometric sequence: sum = 9.9456 sum of arithmetic sequence: sum = 9.9456 sum of geometric sequence: sum = 5.2416 sum of sequence which is neither arithmetic nor geometric; sum = 3.8416

Solution

The sum of geometric sequence (7/5) + (7/5)^2 + (7/5)^3 + (7/5)^4

a = (7/5)

r = (7/5)

S = a(1 - r^n)/(1 - r) = (7/5)*[(1 - (7/5)^4)/(1 - (7/5))] = (7/5)*(-2.8416/-0.4) = 9.9456