sequene problem

[defeated_soldier]

whats the 288th term of the series 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,...... ?

a)24
b)22
c)21
d)20


i see a pattern that if the number is 5 then there is 5 , 5's...similary for 2,3 also
but that does not help me to solve this problem .
i am clueless in solving this problem.
In fact , i am stuck how do i progress ...i know all the formula but i am not sure how and where to plug the formula in this problem.


can you help me to resolve this problem ?

please dont just put your solution .i want to learn the technique ....i want to see ,how you are attacking this problem ....i want to catch your way of thinking .....so step by step approach will help me to master that ...so please explain your solution


thank you for your time

 

[Denis]

whats the 288th term of the series 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,...... ?

Hey, how you doing Mathsoldier?

Notice that the "same numbers" end at terms # 1,3,6,10,15 ...
1[1],2,2[3],3,3,3[6],4,4,4,4[10],5,5,5,5,5[15], ....

1,3,6,10,15 ... are the triangular numbers, right?
You should be ok now: you said you knew all the formulas...

 

[pka]

Using the ceiling function, \(\displaystyle \left\lceil x \right\rceil\) the first integer not exceeded by x, then each term of the sequence is given by:\(\displaystyle \L\;\; S_k = \left\lceil {\frac{-1+{\sqrt {1 + 8k} }}{2}} \right\rceil .\)