For a sequence `{a_n}, a_1 = 2` and `a_(n+1)/a_n=1/3` then `sum_(r=1)^20 a_r` is

For a sequence, if a_(1)=2 and (a_(n+1))/(a_(n))=(1)/(3). Then, sum_(r=1)^(20) a_(r) is

If a_n = n (n!) , then sum_(r=1)^100 a_r is equal to

A_1 A_2 A_3............A_n is a polygon whose all sides are not equal, and angles too are not all equal. theta_1 is theangle between bar(A_i A_j +1) and bar(A_(i+1) A_(i +2)),1 leq i leq n-2.theta_(n-1) is the angle between bar(A_(n-1) A_n) and bar(A_n A_1), while theta_n, is the angle between bar(A_n A_1) and bar(A_1 A_2) then cos(sum_(i=1)^n theta_i) is equal to-

The Fibonacci sequence is defined by 1 = a_1= a_2 and a_n=a_(n-1)+a_(n-2) , n>2 . Find (a_(n+1))/a_n , for n = 1, 2, 3, 4, 5

If the sequence {a_n}, satisfies the recurrence, a_(n+1) = 3a_n - 2a_(n-1), n ge2, a_0 = 2, a_1 = 3, then a_2007 is

The Fibonacci sequence is defined by 1=a_1=a_2 and a_n=a_(n-1)+a_(n-2),n >2 . Find (a_(n+1))/(a_n), for n = 1, 2, 3, 4, 5.

The Fibonacci sequence is defined by 1=a_1=a_2 and a_n=a_(n-1)+a_(n-2),n >2 . Find (a_(n+1))/(a_n), for n = 1, 2, 3, 4, 5.

The Fibonacci sequence is defined by 1=a_1=a_2 and a_n=a_(n-1)+a_(n-2),n >2 . Find (a_(n+1))/(a_n), for n = 1, 2, 3, 4, 5.

Find the first five terms of the following sequence . a_1 = 1 , a_2 = 1 , a_n = (a_(n-1))/(a_(n-2) + 3) , n ge 3 , n in N