let `a_1,a_2,a_3,...........,`be an `AP` such that `(a_1+a_2+a_3+...........+a_p)/(a_1+a_2+a_3+...........+a_q)=p^3/q^3`,`(p!=q)` then find `a_6/a_21=?`

Let a_1,a_2,a_3,...... be an A.P. such that [a_1+a_2+......+a_p]/[a_1+a_2+a_3+......+a_q]=p^3/q^3 ; p!=q .Then a_6/a_[21] is equal to:

For the A.P., a_1, a_2,a_3, ............., if a_4/a_7= 2/3 , find a_6/a_8 .

Let a_1 , a_2 , a_3,.... be terms of an A.P. if (a_1 + a_2 +....+ a_p)/(a_1 + a_2 +...+ a_q) = p^2/q^2. p ne q then a_6/a_21 equals

If a_1, a_2,a_3,..........., a_n be an A.P. of non-zero terms, prove that : 1/(a_1 a_2)+1/(a_2 a_3)+ ............. + 1/(a_(n-1) a_n)= (n-1)/(a_1 a_n) .

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?

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, be terms of an A.P. and (a_1+a_2+.....+a_p)/(a_1+a_2+.....+a_q)=(p^2)/(q^2), p!=q ,t h e n(a_6)/(a_(21)) equals to (a).41/11 (b). 7/2 (c). 2/7 (d). 11/41

If a_1, a_2, a_3, be terms of an A.P. and (a_1+a_2+.....+a_p)/(a_1+a_2+.....+a_q)=(p^2)/(q^2), p!=q ,t h e n(a_6)/(a_(21)) equals to (a).41/11 (b). 7/2 (c). 2/7 (d). 11/41

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

If a_1, a_2, a_3, be terms of an A.P. if (a_1+a_2+...+a_p)/(a_1+a_2+...+a_q)=(p^2)/(q^2), p!=q ,t h e n(a_6)/(a_(21)) equals