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The first two terms of a sequence are 0 ...

The first two terms of a sequence are 0 and 1, The `n ^(th)` terms `T _(n) = 2 T _(n-1) , n ge 3.` For example the third terms `T _(3) = 2 T_(2) - T_(1) = 2 -0=2,` The sum of the first 2006 terms of this sequence is :

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The correct Answer is:
`(2005 xx 2006)/(2)`
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RESONANCE-SEQUENCE & SERIES -EXERCISE -1 PART -I RMO
  1. Given the sequence a, ab, aab, aabb, aaabb,aaabbb,…. Upto 2004 terms, ...

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  2. A sequence a (0) , a(1), a (2), a(3)………..a (n) …. is defined such that...

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  3. The first two terms of a sequence are 0 and 1, The n ^(th) terms T (n)...

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  4. Consider the following sequence :a (1) = a (2) =1, a (i) = 1 + minimum...

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  5. The sum of (1)/( 2sqrt1+1 sqrt2 ) + (1)/( 3 sqrt2 + 2 sqrt3 ) + (1)/(...

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  6. If f (x) + f (1 - x) is equal to 10 for all real numbers x then f ((1)...

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  7. Consider the sequence 4,4,8,0,2,2,4,6,0,….. where the nth term is the ...

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  8. For some natureal number 'n', the sum of the fist 'n' natural numbers ...

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  9. An arithmetical progression has positive terms. The ratio of the diffe...

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  10. The 12 numbers, a (1), a (2)………, a (12) are in arithmetical progressio...

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  11. Each term of a sequence is the sum of its preceding two terms from the...

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  12. n is a natural number. It is given that (n +20) + (n +21) + ......+ (n...

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  13. In a G.P. of real numbers, the sum of the first two terms is 7. The su...

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  14. In a potato race, a bucket is placed at the starting point, which is 7...

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  15. The coefficient of the quadratic equation a x^2+(a+d)x+(a+2d)=0 are co...

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  16. Find the sum of integers from 1 to 100 that are divisible by 2 or 5...

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  17. The sum of three numbers in A.P. is 27, and their product is 504, find...

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  18. The friends whose ages from a G.P. divide a certain sum of money in pr...

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  19. The roots of the equation x^(5)-40x^(4)+ax^

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  20. Let T(n) denotes the n ^(th) term of a G.P. with common ratio 2 and (l...

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