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t_{n+1} = t_n x t_{n+2} , P_n = product of the first n terms

Source: Netherlands - Dutch NMO 1965 p1

January 31, 2023
recurrence relationProductalgebra

Problem Statement

We consider the sequence t1,t2,t3,...t_1,t_2,t_3,... By PnP_n we mean the product of the first nn terms of the sequence. Given that tn+1=tn⋅tn+2t_{n+1} = t_n \cdot t_{n+2} for each nn, and that P40=P80=8P_{40} = P_{80} = 8. Calculate t1t_1 and t2t_2.
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