In an AP:
(i) Given a=5, d=3, `a_(n) = 50`, find n

Let a_(1), a_(2) ...be positive real numbers in geometric progression. For n, if A_(n), G_(n), H_(n) are respectively the arithmetic mean, geometric mean and harmonic mean of a_(1), a_(2),..., a_(n) . Then, find an expression for the geometric mean of G_(1), G_(2),...,G_(n) in terms of A_(1), A_(2),...,A_(n), H_(1), H_(2),..., H_(n)

Find the respective terms for the following Aps: (i) a_(1) =2, a_(3) = 26 find a_(2) (ii) a_(2) =13, a_(4) = 3 find a_(1), a_(3) (iii) a_(1) =5, a_(4) = -22 find a_(1),a_(3),a_(4),a_(5)

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.

For an A.P., if a = -3 and d = 4 then find t_n

(i)If n(A)=25, n(B)=40, n(A cup B)=50 and n(B')=25," find "n(A cap B) and n(U) . (ii) If n(A)=300, n(A cup B)=500, n(A cap B)=50 and n (B')=350 , find n(B) and n(U) .

Let the sum of the first n terms of a non-constant AP a_(1), a_(2), a_(3)...."be " 50n + (n (n-7))/(2)A , where A is a constant. If d is the common difference of this AP, then the ordered pair (d, a_(50)) is equal to

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,

Find the first 6 terms of the sequence given by a_1=1, a_n=a_(n-1)+2 , n ge 2

If a_(1), a_(2), a_(3), ……. , a_(n) are in A.P. and a_(1) = 0 , then the value of (a_(3)/a_(2) + a_(4)/a_(3) + .... + a_(n)/a_(n - 1)) - a_(2)(1/a_(2) + 1/a_(3) + .... + 1/a_(n - 2)) is equal to