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 .

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 .

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

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

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

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)) .

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."

Consider a sequence {a_n }with a_1=2 and a_n=(a_(n-1)^ 2)/(a_(n-2)) for all ngeq3, terms of the sequence being distinct. Given that a_1 and a_5 are positive integers and a_5lt=162 then the possible value(s) of a_5 can be (a) 162 (b) 64 (c) 32 (d) 2

Let a_1,a_2,a_3…… ,a_n be in G.P such that 3a_1+7a_2 +3a_3-4a_5=0 Then find common ratio of G.P.