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A book is published in three volumes, th...

A book is published in three volumes, the pages being numbered from 1 onwards. The page numbers are continued from the first volume to the second volume to the third. The number of pages in the second volume is 50 more than that in the first volume, and the number pages in the third volume is one and a half times that in the second. The sum of the page numbers on the first pages of the three volumes is 1709. If n is the last page number, what is the largest prime factor of n ?

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RESONANCE-SEQUENCE & SERIES -EXERCISE -2 (PART -I PREVIOUS ASKED QUESTION FOR PRE RMO)
  1. Let S (n ) = sum ( k =0) ^(n) (1)/( sqrt ( k +1) + sqrt k) What is th...

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  2. Let m be the smallest odd positive iteger for which 1 + 2+ …..+ m is a...

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  3. What is the the maximum possibe value of k for which 2013 can be writt...

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  4. The first term of a sequence is 2014. Each succeeding term is the sum ...

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  5. A sequence of positive (a (1), a (2)…a (n)) is called good if a (1) =a...

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  6. A new sequence is obtained from the sequence of positive integers 1,2,...

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  7. Let E(n) denote the sum of the even digits of n. For example, E (1243)...

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  8. Consider the sequence 1,3,3,5,5,5,5,5,7,7,7,7,7,7,7,…… and evaluate it...

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  9. Find the value of the expression ((3 ^(4) + 3 ^(2) +1) .(5 ^(4) + 5 ...

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  10. Let S=1 + (1)/(sqrt2) + (1)/(sqrt3) + (1)/(sqrt99) + (1)/(sqrt100). Fi...

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  11. For positive real numbers x and y, define their special mean to be ave...

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  12. Let u,v,w be real numbers in geometric progression such that u gt v gt...

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  13. Let the sum sum ( n =1) ^(g) (1)/(n ( n +1) ( n +2)) written in its lo...

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  14. Suppose x is a positive real number such that {x}, [x] and x are in th...

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  15. Five distinct 2-digit numbes are in a geometric progression. Find the ...

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  16. Let N = 6 + 66+ 666+…+ 666…66, where there are hundred 6's in the last...

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  17. What is the value of sum (1+j = odd 1 le | lt | le 10) (i +j) - sum(1 ...

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  18. A book is published in three volumes, the pages being numbered from 1 ...

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