`a_(1),a_(2),a_(3)…………,a_(n)` are in `A.P.` and `a_(1)+a_(3)+a_(5)+a_(7)+a_(9)= 20` then `a_(5)` is :

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) =

if a_(1),a_(2),a_(3)……,a_(12) are in A.P and Delta_(1)= |{:(a_(1)a_(5),,a_(1),,a_(2)),(a_(2)a_(6),,a_(2),,a_(3)),(a_(3)a_(7),,a_(3),,a_(4)):}| Delta_(2)= |{:(a_(2)a_(10),,a_(2),,a_(3)),(a_(3)a_(11),,a_(3),,a_(4)),(a_(4)a_(12),,a_(4),,a_(5)):}| then Delta_(1):Delta_(2)= "_____"

STATEMENT-1 : If a, b, c are in A.P. , b, c, a are in G.P. then c, a, b are in H.P. STATEMENT-2 : If a_(1) , a_(2) a_(3) ……..a_(100) are in A.P. and a_(3) + a_(98) = 50 " then" a _(1) + a_(2) +a_(3) + ….+ a_(100) = 2500 STATEMENT-3 : If a_(1) , a_(2) , ....... ,a_(n) ne 0 then (a_(1) + a_(2)+ a_(3) + .......+ a_(n))/(n) ge (a_(1) a_(2) .........a_(n) )^(1//n)

If a_(1),a_(2),a_(3),a_(4),a_(5) are in HP, then a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+a_(4)a_(5) is equal to

If a_(1),a_(2)a_(3),….,a_(15) are in A.P and a_(1)+a_(8)+a_(15)=15 , then a_(2)+a_(3)+a_(8)+a_(13)+a_(14) is equal to

If a_(1), a_(2), a_(3),........, a_(n) ,... are in A.P. such that a_(4) - a_(7) + a_(10) = m , then the sum of first 13 terms of this A.P., is:

Let numbers a_(1),a_(2)…a_(16) are in AP and a_(1)+a_(4)+a_(7)+a_(10)+a_(13)+a_(16)=114 then a_(1)+a_(5)+a_(12)+a_(16) is equal to

Let a_(1),a_(2),a_(3),a_(4)anda_(5) be such that a_(1),a_(2)anda_(3) are in A.P., a_(2),a_(3)anda_(4) are in G.P., and a_(3),a_(4)anda_(5) are in H.P. Then, a_(1),a_(3)anda_(5) are in

a_(1),a_(2),a_(3),a_(4),a_(5), are first five terms of an A.P. such that a_(1) +a_(3) +a_(5) = -12 and a_(1) .a_(2) . a_(3) =8 . Find the first term and the common difference.

If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)