Three-consecutive-terms-of-an-A-P-form-the-three-consecutive-terms-of-a-G-P-If-the-common-ratio-of-the-G-P-forms-the-common-difference-of-the-A-P-by-adding-the-first-term-of-the-G-P-to-itself-Find-t

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Question Number 16687 by tawa tawa last updated on 25/Jun/17

Three consecutive terms of an A.P form the three consecutive terms of a G.P, If the common ratio of the G.P forms the common difference of the A.P by adding the first term of the G.P to itself. Find the sum of the fifth term of the G.P.

$$\mathrm{Three}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}\:\mathrm{form}\:\mathrm{the}\:\mathrm{three}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{G}.\mathrm{P}, \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{common}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{G}.\mathrm{P}\:\mathrm{forms}\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{A}.\mathrm{P}\:\mathrm{by} \\ $$$$\mathrm{adding}\:\mathrm{the}\:\mathrm{first}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{G}.\mathrm{P}\:\mathrm{to}\:\mathrm{itself}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{fifth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{G}.\mathrm{P}. \\ $$

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Three-consecutive-terms-of-an-A-P-form-the-three-consecutive-terms-of-a-G-P-If-the-common-ratio-of-the-G-P-forms-the-common-difference-of-the-A-P-by-adding-the-first-term-of-the-G-P-to-itself-Find-t

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