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Top Q&A: The 1000th term of sequence 1,2,2,3,3....Is?

(0)
May 22, 2009

 

Confused about the 1000th term of sequence 1,2,2 3,3.3,4,4,4... or propagation of electromagnetic (EM) waves?

 

Curious readers posed these questions in Topper's Ask The Expert section, and received an answer within three working days!

 

 

Subject: Maths

 

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

 

Posted by: Thebluebloo

 

 

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

 

 

Term value

Number of times

Cumulative Frequency

1

1 1

2

2 3

3

3

6

4

4

10

.. .. ..

n

n

n(n+1)/2

 

 

 

 

 

 

 

 

 

 

 

 

Consider 1,3,6,10,...

Difference of the consecutive terms is an AP.

So applying the method of difference we get,

Tn = n (n+1) / 2

We need to find 1000th term

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...