For an A.P. a n , let α = ∑ r = 1 100 a 2 r and β = ∑ r = 1 100 a 2 r − 1 . What is its common difference?

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MathematicsSequence & SeriesA.P.Medium2 minQB

MathematicsMediumsingle choice

For an A.P. $a_{n}$ , let $α = \sum_{r = 1}^{100} a_{2 r}$ and $β = \sum_{r = 1}^{100} a_{2 r - 1}$ . What is its common difference?

Answer:

Solution:

Pairing adjacent even and odd terms gives $α - β = 100 d$ , so $d = (α - β) /100$ , not (A), (B) or (C) in general.

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:A.P.

⏱ 2mℹ️ Source: QB

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