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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??
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
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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