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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesSpecial sequences/seriesMedium2 minQB

MathematicsMediummultiple choice

Let ${a_{n}}$ be a sequence such that $a_{0} = 1, a_{1} = 0, a_{n} = 3 a_{n - 1} - 2 a_{n - 2}$ . The correct statement is:

Options:(select one or more)

Answer:

A, B, C, D

Solution:

$a_{n} - 2 a_{n - 1} = a_{n - 1} - 2 a_{n - 2} = \dots = a_{1} - 2 a_{0} = - 2$ . So $a_{n} - 2 = 2 (a_{n - 1} - 2)$ and $a_{n} - 2 = (a_{0} - 2) 2^{n} = - 2^{n}$ , giving $a_{n} = 2 - 2^{n}$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:Special sequences/series

⏱ 2mℹ️ Source: QB

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