



 
Hi Jessica. In a geometric series, consecutive terms are derived by multiplying the previous term by some constant factor. So that means the ratio between adjacent terms is a constant. In your case, 18/54 = 1/3, so Each geometric series starts with an initial value which we can call A, and has a common factor we can call F. That means the second value is AF, the third value is AF^{2}, the fourth value is AF^{3} and so on. In general, the "n"th value is AF^{n1}. Your sequence has F = 1/3, but what is A? You know that the 15th term is 54, so 54 = A(1/3)^{14}. Thus A = 54(3)^{14}. Now if you add up the second through fifth terms, you have AF + AF^{2} + AF^{3} + AF^{4} which is just A (F + F^{2} + F^{3} + F^{4}). Now you can substitute in your values of A and F to solve your problem. Hope this helps,  


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