Home
Class 12
MATHS
Consider the sequence 1,2,2,3,3,3,"……", ...

Consider the sequence `1,2,2,3,3,3,"……",` where n occurs n times that occuts as 2011th rerms is

A

61

B

62

C

63

D

64

Text Solution

Verified by Experts

The correct Answer is:
C
The last 4 occurs as `1+2+3+4+=10th` term. The last n occurs as `((n(n+1))/(2))^(th)` term, the last 62 occurs as
`((63xx63)/(2))^(th)=1953rd` term and the last 63 occurs as
`((64xx64)/(2))^(th)=2016th` term.
`:. 63` occurs from 1954th term to 2016th term.
Hence, `(2011)^(th)` term os 63.
Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

Consider a sequence whose sum to n terms is given by the quadratic function Sn= 3n^2 +5n . Then sum of the squares of the first 3 terms of the given series is

For the S_(n)=3n^(2)+5n sequence, the number 5456 is the

Knowledge Check

  • 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

  • If in the expansion (1+x)^(n) the 5^(th ) term is 4 times the 4^(th) term and the 4^(th) term is 6 times the 3^(rd)' term, then n=

    A
    9
    B
    10
    C
    11
    D
    15

    • Similar Questions

    Explore conceptually related problems

    First term of a sequence is 1 and the (n+1)th term is obtained by adding (n+1) to the nth term for all natural numbers n, the 6th term of the sequence is

    Find 17^(th) term of sequence whose n^(th) term is given by a_(n) = 4n-3 ?

    Show that the the sequence defined by T_(n) = 3n^(2) +2 is not an AP.

    If the nth term of the sequence is a_ n =4n -3 then find 17th term

    Write the 5^(th) terms of the sequences whose n^(th) term is a_(n) = 2^(n) ?

    The sequence a_(1),a_(2),a_(3),".......," is a geometric sequence with common ratio r . The sequence b_(1),b_(2),b_(3),".......," is also a geometric sequence. If b_(1)=1,b_(2)=root4(7)-root4(28)+1,a_(1)=root4(28)" and "sum_(n=1)^(oo)(1)/(a_(n))=sum_(n=1)^(oo)(b_(n)) , then the value of (1+r^(2)+r^(4)) is

    Home
    Profile