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AP - Plz explain the sum

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by Anurag@Gurome » Fri Sep 02, 2011 2:59 am
anjana_gmat wrote:Q. In the sequence 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8,......................., find the 1035th term of the sequence.
Note that,
  • 1st term of the sequence = 1 = 2^0
    2nd term of the sequence = 2 = 2^1
    3rd term of the sequence = 2 = 2^1
    4th term of the sequence = 4 = 2^2
    5th term of the sequence = 4 = 2^2
    6th term of the sequence = 4 = 2^2
    etc...
Hence, n-th term of the sequence = greatest integral power of 2 less than n

Therefore, 1035th term of the sequence = greatest integral power of 2 less than 1035 = 1024 = 2^10
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by Abhishek009 » Fri Sep 02, 2011 6:39 am
anjana_gmat wrote:Q. In the sequence 1, 2, 2, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8,......................., find the 1035th term of the sequence.
1 will have 1 terms

2 will have 2 terms

4 will have 4 terms

8 will have 8 terms

16 will have 16 terms

32 will have 32 terms

64 will have 64 terms

128 will have 128 terms

256 will have 256 terms

512 will have 512 terms

Add them up U get 1023

So definitely U need to proceed further


Go further 1024 will have 1024 terms


Hence U can confidently claim the 1035th term of the sequence will be 1024.....
Abhishek
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