Cool problem! I solved it using S_n = a(1-r^n)/(1-r) for the 2 given cases with n = 2 and 4. Factoring (1-r^4) and canceling gives 5.1968 = a(1+r)(1+r^2). Similar approach for S_2 gives 4.48 = a(1+r). Then I substituted 4.48 in place of the a(1+r) in my S_4 equation to short cut straight to 5.1968 = 4.48(1+r^2)
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