A positive sequence has each term from the third onward equal to the sum of all preceding terms. If its first term is 1 and its seventh is 1000, find the second.

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From the third term onward each term doubles the previous one: t 3 ​ = t 1 ​ + t 2 ​ and t 7 ​ = 16 ( t 1 ​ + t 2 ​ ) = 1000 . Hence t 2 ​ = 1000/16 − 1 = 123/2 .

Mathematics - Sequence & Series Question with Solution | TestHub

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