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In the sequence 1,2,2,3,3,3,4,4,4,4,...........where n consecutive terms have the value n, the 150 th term, is a)17 b)16 c)18 d)none of these How to solve these types of sums??

In the sequence 1,2,2,3,3,3,4,4,4,4,...........where n consecutive terms have the value n, the 150th term, is 
a)17
b)16
c)18
d)none of these
How to solve these types of sums??

Grade:

2 Answers

Arun
25750 Points
5 years ago
Dear Student
 
Notice that the last instance of a particular integer, i, occurs at the term that is the sum of all integers up to i.
For example, the last 3 is the sixth term and Σi (i=1 to 3)=6.  If you think about it for a bit this is obvious.
 
So let's set up an equation.  Σi (1 to m)=150.  If such an m existed, then it would be the last instance of the inetger m and the 150th term.  A little thought lures us to the inequality 150
 
150
 
300
 
We could use the quadratic formula, but I would just estimate...17 mostly from the first inequality.
 
302
 
17 is the 150th term
Meghendra Agrawal
8 Points
5 years ago
Inequalities are not displayed..the signs are missing.Please show the later part again..Also please tell how did you do the estimation??

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