The sequence `a_1, a_2, a_3, ,..............a_98` satisfies the relation `a_(n+1) = a_n + 1` for `n = 1 ,2,3,........... 97` and has the sum equal to 4949, Evaluate `suma_2k`

The sequence a_(1), a_(2), a_(3), ..... a_(98) satisfies the relation a_(n + 1) = a_(n) +1" for " n = 1, 2, 3,..... 97 and has the sum equal to 4949. Evaluate sum_(k=1)^(49) a_(2k)

A sequence of no. a_1,a_2,a_3 ..... satisfies the relation a_n=a_(n-1)+a_(n-2) for nge2 . Find a_4 if a_1=a_2=1 .

A sequence of numbers a_0,a_1,a_2,a_3 , ........ satisfies the relation a_n^2-a_(n-1)a_(n+1)=(-1)^n . Find a_3 , given a_0=1 and a_1=3 .

A sequence of number a_1, a_2, a_3,…..,a_n is generated by the rule a_(n+1) = 2a_(n) . If a_(7) - a_(6) = 96 , then what is the value of a_(7) ?

A sequence of positive integers a_1 , a_2, a_3, …..a_n is given by the rule a_(n + 1) = 2a_(n) + 1 . The only even number in the sequence is 38. What is the value of a_2 ?

"If "a_1,a_2,a_3,.....,a_n" are in AP, prove that "a_(1)+a_(n)=a_(r)+a_(n-r+1)""

If a_1, a_2 , ............, a_n are in A.P.with common difference d ne 0 , then [sin d] [sec a_1 sec a_2 + sec a_2sec a_3+............+ sec a_(n-1) sec a_n] is equal to :

Let a_1, a_2, a_3, ...a_(n) be an AP. then: 1 / (a_1 a_n) + 1 / (a_2 a_(n-1)) + 1 /(a_3a_(n-2))+......+ 1 /(a_(n) a_1) =

A sequence a_1,a_2,a_3, ... is defined by letting a_1=3 a n d a_k=7a_(k-1) for natural numbers k ,kgeq2. Show that a_n=3.7_n-1 for all n in N .

Let the sequence a_1 , a_2 , a_3 ......... a_n form an A.P. then a_1^2 - a_2^2 + a_3^2 - a_4^2 +.....+ a_(2n-1)^2 - a_(2n)^2 is equal to:- (1) n/(2n-1)(a_1^2-a_(2n)^2) (2) (2n)/(n-1)(a_(2n)^2-a_1^2) (3) n/(n+1)(a_1^2+a_(2n)^2) (4)none of these