Let u n -1-2 u n -1- n -0-1-2- - and u 0-0- Then u 10 would be nearest to- CAT 1993A- 1023B- 2047C- 4095D- 8195

The correct option is A 1023Ans: (a) u n+1 = 2un + 1 (n = 0, 1, 2,…..)Put n = 0, u1 = 1n = 1, u2 = 3n = 2, u3 = 7n = 3, u4 = 15n = 4, u5 = 31Seeing the pattern ...

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Quantitative Aptitude

A.M Greater than or Equal to G.M

Let u n +1=2 ...

Question

Let u _n+1 = 2u_n +1, (n = 0, 1, 2,…) and u₀ = 0. Then u₁₀ would be nearest to: (CAT 1993)

1023

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2047

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4095

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8195

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Solution

The correct option is A 1023
Ans: (a)
u _n+1 = 2u_n + 1 (n = 0, 1, 2,…..)
Put n = 0, u₁ = 1
n = 1, u₂ = 3
n = 2, u₃ = 7
n = 3, u₄ = 15
n = 4, u₅ = 31
Seeing the pattern it is clear that u_n = 2ⁿ – 1
Hence u₁₀ = (2)¹⁰ – 1 = 1,023.

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Let u n+1 = 2un +1, (n = 0, 1, 2,…) and u0 = 0. Then u10 would be nearest to: (CAT 1993)

The correct option is A 1023Ans: (a) u n+1 = 2un + 1 (n = 0, 1, 2,…..)Put n = 0, u1 = 1n = 1, u2 = 3n = 2, u3 = 7n = 3, u4 = 15n = 4, u5 = 31Seeing the pattern it is clear that un = 2n – 1Hence u10 = (2)10 – 1 = 1,023.

Let u _n+1 = 2u_n +1, (n = 0, 1, 2,…) and u₀ = 0. Then u₁₀ would be nearest to: (CAT 1993)

The correct option is A 1023
Ans: (a)
u _n+1 = 2u_n + 1 (n = 0, 1, 2,…..)
Put n = 0, u₁ = 1
n = 1, u₂ = 3
n = 2, u₃ = 7
n = 3, u₄ = 15
n = 4, u₅ = 31
Seeing the pattern it is clear that u_n = 2ⁿ – 1
Hence u₁₀ = (2)¹⁰ – 1 = 1,023.