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- 2047B- 1023C- 4095D- 8195

The correct option is B 1023u_n+1=2u_n+1, (n=0,1,2,....) Put n = 0, u_1 = 1 n = 1, u_2 = 3 n = 2, u_3 = 7 n = 3, u_4 = 15 n = 4, u_5 = 31 Seeing the patt ...

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Quantitative Aptitude

Functions

Let u n +1=2 ...

Question

Let $u_{n + 1} = 2 u_{n} + 1, (n = 0, 1, 2, . . . .)$ and $u_{0} = 0$ . Then $u_{10}$ 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
$u_{n + 1} = 2 u_{n} + 1, (n = 0, 1, 2, . . . .)$

Put n = 0, $u_{1}$ = 1

n = 1, $u_{2}$ = 3

n = 2, $u_{3}$ = 7

n = 3, $u_{4}$ = 15

n = 4, $u_{5}$ = 31

Seeing the pattern it is clear that $u_{n} = 2^{n} - 1$

Hence , $u_{10} = (2)^{10} - 1 = 1, 023.$

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Let un+1=2un+1, (n=0,1,2,....) and u0=0. Then u10would be nearest to: (CAT 1993)

The correct option is A 1023un+1=2un+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 un=2n−1 Hence ,u10=(2)10−1=1,023.

Let $u_{n + 1} = 2 u_{n} + 1, (n = 0, 1, 2, . . . .)$ and $u_{0} = 0$ . Then $u_{10}$ would be nearest to: (CAT 1993)

The correct option is A 1023
$u_{n + 1} = 2 u_{n} + 1, (n = 0, 1, 2, . . . .)$

Put n = 0, $u_{1}$ = 1

n = 1, $u_{2}$ = 3

n = 2, $u_{3}$ = 7

n = 3, $u_{4}$ = 15

n = 4, $u_{5}$ = 31

Seeing the pattern it is clear that $u_{n} = 2^{n} - 1$

Hence , $u_{10} = (2)^{10} - 1 = 1, 023.$