IIT JEE , AIEEE Forum - Mathematics , Algebra

abh2_mkp2

How to find the 11th term in series
1,2,2,3,3,3,4,4,4,4,...........

priyesh

see the series is like this

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

now from here we see that 11th term is 5

edison

Q) How to find the 11th term in series
1,2,2,3,3,3,4,4,4,4,...........

Solution) Here in the series,

1 occurs 1time

2 occurs 2 times

3 occurs 3 times

.

n occurs n times

so 1,2,2,3,3,3,4,4,4,4,5(11th term),5,5,5,5

So 11th term is 5.

edison

The better question would be rather what will be the nth term in the series?

sailesh_07

ans is so simple man, 1 is writen once,2 twice 3 thrice and four four times. this comes to 10 terms. hence the next set terms in this series is 5 repeated 5 times. therefore the 11th term is five.
rate me if you like my reply

nick

this q can also be done via inequality..

see the series
1
2,2
3,3,3,....
....

that means whae we have to find the 11 term it SHOULD BE THE SUM OF
1,2,3,4 i.e. the no. of terms corresponding to 1,2....

BUT it is not always that 1,2,3,4,5... will give the desired sum like in this case

so..we have the inequality
11=< n/2(2 +n-1) summing it

22=or n^2 +n-22>=0
now this is -1+root89/2 u see r00t 89 is more than 9
hence the root
if worked is little more than 4 now it can surely not be 4 so it has to the
NEXT INTEGER THAT IS 5,which is the ans,

this method is useful when u have to find ans for huge no.

Ask & Discuss Questions with Community & Experts