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If 2n +1Pn : 2n–1Pn = 3 : 5, then n equals 

(a) 2 

(b) 3 

(c) 6 

(d) 4

1 Answer

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Best answer

(d) 4

2n +1Pn : 2n–1Pn = 3 : 5

⇒ (4n2 + 2n) 5 = 3 × (n3 + 3n2 + 2n) 

⇒ 20n2 + 10n = 3n3 + 9n2 + 6n 

⇒ 3n3 – 11n2 – 4n = 0 

⇒ n(3n2 – 11n – 4) = 0 

⇒ n(3n2 – 12n + n – 4) = 0 

⇒ n(3n(n – 4) + 1(n – 4)) = 0 

⇒ n = 0 or 4 or \(-\frac13\)  

Ignoring n = 0, \(-\frac13\) as these are in admissible values, we have n = 4.

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