In a G,P, `T_(2) + T_(5) = 216 and T_(4) : T_(6) = 1:4` and all terms are integers, then find its first term :

In an A.P., if T_(1) +T_(5)+ T_(10) +T_(15)+ T_(20) + T_(24) = 225, find the sum of its 24 terms.

Let {t_(n)} is an A.P If t_(1) = 20 , t_(p) = q , t_(q) = p , find the value of m such that sum of the first m terms of the A.P is zero .

The first two terms of a sequence are 0 and 1, The n ^(th) terms T _(n) = 2 T _(n-1) - T _(n-2) , n ge 3. For example the third terms T _(3) = 2 T_(2) - T_(1) = 2 -0=2, The sum of the first 2006 terms of this sequence is :

If t_(n) represents nth term of an A.P., t_(2)+t_(5)-t_(3)= 10 and t_2 + t_9= 17. find its first term and its common difference.

In a harmonic progression t_(1), t_(2), t_(3),……………., it is given that t_(5)=20 and t_(6)=50 . If S_(n) denotes the sum of first n terms of this, then the value of n for which S_(n) is maximum is

If t_(8)=4 and t_(12)=-2 , find the first three terms of the arithmetic sequence.

If the 10 t h term of an A.P. is 21 and the sum of its first ten terms is 120, find its n t h term.

In an A.P., if p^(t h) term is 1/q and q^(t h) term is 1/p , prove that the sum of first pq terms is 1/2(p q+1), where p!=q .

The first four terms of a sequence are given by T_(1)=0, T_(2)=1, T_(3) =1, T_(4) =2. The general terms is given by T_(n)=Aalpha ^(n -1) +B beta ^(n-1) where A,B alpha, beta are independent of a and A is positive. The value of 5 (A^(2) + B ^(2) is equal to :

In an A.P., if the 5t h and 12 t h terms are 30 and 65 respectively, what is the sum of first 20 terms?