Find the 1000th term of sequence 1,2,2,3,3,3,4,4,4,4,...

Asked by thebluebloo | 13th Apr, 2009, 08:37: AM

Expert Answer:

1,2,2,3,3,3,4,4,4,4,5,5,5,5,5.......................................

Term value         Number of times  Cumulative Frequency Difference
1 1 1 0
2 2 3 2
3 3 6 3
4 4 10 4
.. .. .. ..
n n n(n+1)/2 n

The series of difference term is an AP.

Tn = n (n+1) / 2

1000 = n(n+1)/2

n = 44.2

Its nearest integral value is 44.

So, 44 is the value of the 1000th term of the series 1,2,2,3,3,3,4,4,4,4................

 

Answered by  | 19th May, 2009, 01:59: PM

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