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in sequence 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5......... find 150th term
Hope this will help you , this series can be converted into an easier one if we write the frequencies of the given nos. let'' start with a smaller no. , say the 5th term. thus, the cumulative frequency of nth no. will be the sum of the n terms,i.e., {n(n+1)}/2. so, coming to our example, equating 7 to the sum given:- 5= {n(n+1)}/2 or n2 +n -10=0 this gives:- n= [-1+(1+40)1/2]/2 {since n cannot be -ve, so +ve sqrt.} this gives, 3>n>2. thus, the cumulative frequency of 2 is less than 5 and that of 3 is more than 5. so, n=3. which is correct now, coming back to the problem , we equate 150 to the sum given thus, 150= {n(n+1)}/2 or n2 +n - 300=0 Now factorise and conside the +ve root and not the -ve root .
Hope this will help you ,
this series can be converted into an easier one if we write the frequencies of the given nos.
let'' start with a smaller no. , say the 5th term.
thus, the cumulative frequency of nth no. will be the sum of the n terms,i.e., {n(n+1)}/2.
so, coming to our example, equating 7 to the sum given:-
5= {n(n+1)}/2 or n2 +n -10=0
this gives:- n= [-1+(1+40)1/2]/2 {since n cannot be -ve, so +ve sqrt.}
this gives, 3>n>2. thus, the cumulative frequency of 2 is less than 5 and that of 3 is more than 5. so, n=3. which is correct
now, coming back to the problem , we equate 150 to the sum given
thus, 150= {n(n+1)}/2 or n2 +n - 300=0
Now factorise and conside the +ve root and not the -ve root .
Didn''t it help you?
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