For arithmetic sequence `a_(1),a_(2),a_3` ........ If `a_(1)+a_(5)+a_(10)+a_(15)+a_(20)+a_(24)= 225` then `s_(24) = ............ `

Find the sum of first 24 terms of the A.P. a_(1) , a_(2), a_(3) ...., if it is know that a_(1) + a_(5) + a_(10) + a_(15) + a_(20) + a_(24) = 225

If the arithmetic mean of a_(1),a_(2),a_(3),"........"a_(n) is a and b_(1),b_(2),b_(3),"........"b_(n) have the arithmetic mean b and a_(i)+b_(i)=1 for i=1,2,3,"……."n, prove that sum_(i=1)^(n)(a_(i)-a)^(2)+sum_(i=1)^(n)a_(i)b_(i)=nab .

Let b_(i)gt1" for "i=1,2,"......",101 . Suppose log_(e)b_(1),log_(e)b_(2),log_(e)b_(3),"........"log_(e)b_(101) are in Arithmetic Progression (AP) with the common difference log_(e)2 . Suppose a_(1),a_(2),a_(3),"........"a_(101) are in AP. Such that, a_(1)=b_(1) and a_(51)=b_(51) . If t=b_(1)+b_(2)+"........."+b_(51)" and " s=a_(1)+a_(2)+"........."+a_(51) , then

Let a_(1),a_(2),"...." be in AP and q_(1),q_(2),"...." be in GP. If a_(1)=q_(1)=2 " and "a_(10)=q_(10)=3 , then

The number of all possible 5-tuples (a_(1),a_(2),a_(3),a_(4),a_(5)) such that a_(1)+a_(2) sin x+a_(3) cos x + a_(4) sin 2x +a_(5) cos 2 x =0 hold for all x is

Find the respective terms for the following Aps: (i) a_(1) =2, a_(3) = 26 find a_(2) (ii) a_(2) =13, a_(4) = 3 find a_(1), a_(3) (iii) a_(1) =5, a_(4) = -22 find a_(1),a_(3),a_(4),a_(5)

Suppose four distinct positive numbers a_(1),a_(2),a_(3),a_(4) are in G.P. Let b_(1)=a_(1),b_(2)=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.

For arithmetic sequence a_(8) =23 common difference d = 5 then a = ...............

If a_(1), a_(2), a_(3) ,…., a_(n) are the terms of arithmatic progression then prove that (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) + (1)/(a_(3)a_(4)) + ….+ (1)/(a_(n-1) a_(n)) = (n-1)/(a_(1)a_(n))

What does a_(1) + a_(2) + a_(3) + …..+ a_(n) represent