Home
Class 12
MATHS
Let {an}(ngeq1) be a sequence such that ...

Let `{a_n}(ngeq1)` be a sequence such that `a_1=1,a n d3a_(n+1)-3a_n=1fora l lngeq1.` Then find the value of `a_(2002.)`

Text Solution

Verified by Experts

The correct Answer is:
668
`a_(1)=1`
`3a_(n+1)-3a_(n)=1`
`thereforea_(n+1)=(2a_(n)+1)/3=a_(n)+1/3`
`thereforea_(2)=a_(1)+1/3=1+1/3`
`thereforea_(3)=a_(2)+1/3=a_(1)+1/3+1/3=1+2/3`
`thereforea_(4)=a_(3)+1/3=1+2/3+1/3=1+3/3`
…. ….. …..
…. ….. ……
`thereforea_(2002)=1+2001/3=1+667=668`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.2|10 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.3|9 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLES 5.15|1 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

Let {a_n}(ngeq1) be a sequence such that a_1=1,a n d3a_(n+1)-3a_n=1 for all ngeq1. Then find the value of a_(2002.)

If a_(n+1)=1/(1-a_n) for n>=1 and a_3=a_1 . then find the value of (a_2001)^2001 .

Consider the sequence defined by a_n=a n^2+b n+c dot If a_1=1,a_2=5,a n da_3=11 , then find the value of a_(10)dot

Let lta_ngt be the sequence defined by a_1=3 and a_n =3a_(n-1)+2 for all n gt1 ..Find a_3 .

If "^(2n+1)P_(n-1):^(2n-1)P_n=3:5, then find the value of n .

If a_(1) = 2 and a_(n) - a_(n-1) = 2n (n ge 2) , find the value of a_(1) + a_(2) + a_(3)+…+a_(20) .

Let a_(0)=0 and a_(n)=3a_(n-1)+1 for n ge 1 . Then the remainder obtained dividing a_(2010) by 11 is

For the sequence {u_(n)} if u_(1) = (1)/(2) and u_(n+1) = (u_(n))/(1+2u_(n))(n ge 1) , find the value of u_(96) .

If a_(1)=1 and a_(n+1)=(4+3a_(n))/(3+2a_(n)),nge1"and if" lim_(ntooo) a_(n)=a,"then find the value of a."

For the sequence {u_(n)} if u_(1) = (1)/(4) and u_(n+1) = (u_(n))/(2+u_(n)) , find the value of (1)/(u_(50)) .