If `a_(1)=1, a_(2)=1 and a_(n)=2a_(n-1)+a_(n-2), nge3, ninN`, then find the first six terms of the sequence.

If a_(1)=-1 and a_(n)=(a_(n-1))/(n+2) then the value of a_(4) is ____.

If a_(1) = 4 and a_(n + 1) = a_(n) + 4n for n gt= 1 , then the value of a_(100) is

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."

The Fibonacci sequence is defined by 1 = a_(1) = a_(2) and a_(n) = a_(n - 1) + a_(n - 2),n gt 2 . Find a_(n + 1)/a_(n) , for n = 1, 2, 3, 4, 5,

If a_(1), a_(2), a_(3) ,... are in AP such that a_(1) + a_(7) + a_(16) = 40 , then the sum of the first 15 terms of this AP is

Let a_(1), a_(2), a_(3), a_(4) be in A.P. If a_(1) + a_(4) = 10 and a_(2)a_(3) = 24 , them the least term of them is

If a_(1), a_(2) …… a_(n) = n a_(n - 1) , for all positive integer n gt= 2 , then a_(5) is equal to

Show that a_(1), a_(2) ,……, a_(n) …. Form an AP where a_(n) is defined as below: (i) a_(n) = 3 + 4n , (ii) a_(n) = 9-5n Also find the sum of the first 15 terms in each case.

A sequence of integers a_1+a_2++a_n satisfies a_(n+2)=a_(n+1)-a_nforngeq1 . Suppose the sum of first 999 terms is 1003 and the sum of the first 1003 terms is -99. Find the sum of the first 2002 terms.