If a(1)a(2)a(3)…….a(9) are in A.P. then ...

If `a_(1)a_(2)a_(3)…….a_(9)` are in A.P. then the value of `|(a_(1),a_(2),a_(3)),(a_(4),a_(5),a_(6)),(a_(7),a_(8),a_(9))|` is

`(9)/(2)(a_(1)+a_(9))`

`a_(1)+a_(9)`

`log_(e)(log_(e))`

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8,A_(1),A_(2),A_(3),24.

If a_(1),a_(2) , a_(3),"……..",a_(n) are in H.P. , then : (a_(1))/( a_(2) + a_(3) +"........."+a_(n)),(a_(2))/(a_(1) + a_(3)+"..........."+a_(n)),"......",(a_(n))/(a_(1)+a_(2)+"........"a_(n-1)) are in :

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)

If a_(1), a_(2), a_(3)"….." are in G.P. , then the value of Delta= |{:(log a_(n),loga_(n+1),loga_(n+2)),(log a_(n+3),loga_(n+4),loga_(n+5)),(loga_(n+6),loga_(n+7),loga_(n+8)):}| is :

If a_(1), a_(2) ,a_(3)"….." is an 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 :

If a_(r ) gt 0, r in N and a_(1), a_(2) , a_(3) ,"……..",a_(2n) are in A.P. then : (a_(1) + a_(2n))/( sqrt( a_(1))+ sqrt(a_(2))) + ( a_(2) + a_(2n-1))/(sqrt(a_(2)) + sqrt(a_(3)))+"......"(a_(n)+a_(n+1))/(sqrt(a_(n))+sqrt(a_(n+1))) is equal to :

Suppose four distinct positive numbers a_(1),a_(2),a_(3),a_(4) are in G.P. Let b_(1)=a_(1)+,a_(b)=b_(1)+a_(2),b_(3)=b_(2)+a_(3)andb_(4)=b_(3)+a_(4) . Statement -1 : The numbers b_(1),b_(2),b_(3),b_(4) are neither in A.P. nor in G.P. Statement -2: The numbers b_(1),b_(2),b_(3),b_(4) are in H.P.

If a_(1),a_(2),a_(3),"........",a_(n) are in AP with a_(1)=0 , prove that (a_(3))/(a_(2))+(a_(4))/(a_(3))+"......"+(a_(n))/(a_(n-1))-a_(2)((1)/(a_(2))+(1)/(a_(3))"+........"+(1)/(a_(n-2)))=(a_(n-1))/(a_(2))+(a_(2))/(a_(n-1)) .

If a_(1) , a_(2), "……………" a_(n) are in H.P., then the expression a_(1) a_(2) + a_(2) a_(3)+"…….."+ a_(n-1) a_(n) is equal to :

If a_(1) , a_(2) , a_(3),"………."a_(n) are in H.P. , then a_(1), a_(2) + a_(2) a_(3) + "………" + a_(n-1)a_(n) will be equal to :

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