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 {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.)

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)=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."

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) .

If a_(1), a_(2) , a_(3),…,a _(n+1) are in A. P. then the value of (1)/(a _(1)a_(2))+(1)/(a_(2)a_(3))+(1)/(a_(3)a_(4))+...+(1)/(a_(n)a_(n+1)) is-

If roots of an equation x^n-1=0a r e1,a_1,a_2,..... a_(n-1), then the value of (1-a_1)(1-a_2)(1-a_3)(1-a_(n-1)) will be n b. n^2 c. n^n d. 0

If a_1+a_2+a_3+......+a_n=1 AA a_i > 0, i=1,2,3,......,n , then find the maximum value of a_1 a_2 a_3 a_4 a_5......a_n .

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

If (1+x-2x^2)^(20)=a_0+a_1x+a_2x^2+a_3x^3+...+a_(40)x^(40), then find the value of a_1+a_3+a_5+...+a_(39)dot