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Question Number 173178 by pete last updated on 07/Jul/22

When the terms of a Geometric Progression (G.P.) with r=2 is added to the corresponding terms of an arithmetic progression (A.P.), a new sequence is formed. If the first terms of the GP and AP are the same and the first three termsof the new sequence are 3, 7 and 11 respectively, find the nth term of the new sequence

$$\mathrm{When}\:\mathrm{the}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{Geometric}\:\mathrm{Progression}\:\left(\mathrm{G}.\mathrm{P}.\right) \\ $$$$\mathrm{with}\:\mathrm{r}=\mathrm{2}\:\mathrm{is}\:\mathrm{added}\:\mathrm{to}\:\mathrm{the}\:\mathrm{corresponding} \\ $$$$\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{arithmetic}\:\mathrm{progression}\:\left(\mathrm{A}.\mathrm{P}.\right), \\ $$$$\mathrm{a}\:\mathrm{new}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{formed}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{first}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{GP}\:\mathrm{and}\:\mathrm{AP}\:\mathrm{are}\:\mathrm{the}\:\mathrm{same}\:\mathrm{and}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{three}\:\mathrm{termsof}\:\mathrm{the}\:\mathrm{new}\:\mathrm{sequence}\:\mathrm{are} \\ $$$$\mathrm{3},\:\mathrm{7}\:\mathrm{and}\:\mathrm{11}\:\mathrm{respectively},\:\mathrm{find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{new}\:\mathrm{sequence} \\ $$

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