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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesA.P.Medium2 minQB

MathematicsMediummultiple choice

Positive terms $a_{1}, .., a_{16}$ form an A.P. with difference d and $a_{1} + a_{4} + a_{7} + a_{10} + a_{13} + a_{16} = 147$ . Which statements hold?

Options:(select one or more)

Answer:

A, B, C, D

Solution:

Pairing terms gives $3 (a_{1} + a_{16}) = 147$ and $2 a_{1} + 15 d = 49$ . These yield $A, B$ and C. All sixteen have mean $49/2$ ; AM-GM bounds their product by $(49/2)^{16}$ , attained for $d = 0$ .

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

⏱ 2mℹ️ Source: QB

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