let `a_1,a_2,a_3.......`be an `AP` such that `(a_1+a_2+............+a_p)/(a_1+a_2+.............+a_q)=p^3/q^3` then `a_/a_21`

FOr an integer nlt2, we have real numbers a_1,a_2,a_3,a_4,..........,a_n such that a_2+a_3+a_4+.......+a_n=a1 and a_1+a_3+a_4+...........+a_n=a_2...............a_1+a_2+a_3+..............+a_(n-1)=a_n what is the value of a_1+a_2+a_3+........+a_n?

If a_1, a_2, a_3 ,........ are in A.P. such that a_1 + a_5 + a_10 + a_15 + a_20 + a_24 = 225 , then a_1 + a_2+ a_3 + ......+ a_23 +a_24 is equal to

Let a_1,a_2,a_3………. be term of an A.P. if (a_1+a_2+….+a_p)/(a_1+a_2+………+a_q)=p^2/q^2 p!=q then a_6/ a_21 euqals (A) 41/11 (B) 11/41 (C) 13/44 (D) 15/41

Let (a_1,a_2,a_3....a_4) be a permutation of (1,2,3....n) for which a_1 > a_2 .a_3 >.........> a_ (a/2) and a_(n/2=1) a_2 >a_3..........>a_((x-2)/2 and a_((n-1)/2 <.... < a_2for n as positive integers. Let the total number of permutation of n be p(n). if 200 < p(n) < 5000. then values of n is /are

If a_1, a_2, a_3, .... a_4001 are terms of an A.P. such that 1/(a_1a_2)+1/(a_2a_3)+1/(a_3a_4)+......1/(a_4000a_4001)=10 and a_2+a_4000=50, then |a_1-a_4001| is equal to

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

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

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