Which rule defines cap s sub n for a_n=5⁢((3)/(4))^n ?

The terms form a geometric sequence with common ratio 3/4. Since the sequence begins at n = 1, its first term is 5(3/4) = 15/4. The sum of the first n terms is (15/4)(1 − (3/4)^n)/(1 − 3/4) = 15(1 − (3/4)^n), which is choice A.

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