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^4_k=1 (2/5)^k sum of arithmetic sequence: sum = 0.6496 sum of geometric sequence: sum = 0.6496 sum of geometric sequence: sum = 0.4256 sum of sequence which is neither arithmetic nor geometric: sum = 0.0256

Solution

(2/5) +(2/5)²+(2/5)³+(2/5)⁴

Here first term is 2/5 and common ratio is 2/5

S₄=(2/5)(1-(2/5)⁴)/(1-2/5) =.6496

Correct option is B