Find the sum of first 24 terms of the A.P. `a_1,a_2, a_3 ......., ` if it is inown that `a_1+a_5+a_(10)+a_(15)+a_(20)+a_(24)=225.`

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 sequence a_1, a_2, a_3,....... a_n ,dot forms an A.P., then prove that a_1^2-a_2^2+a_3^2-a_4^2+.......+ a_(2n-1)^2 - a_(2n)^2=n/(2n-1)(a_1^2-a_(2n)^2)

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) =

Find the indicated terms in each of the following sequences whose nth terms are: a_n=5_n-4; a_(12) and a_(15) a_n=(3n-2)/(4n+5); a_7 and a_8 a_n=n(n-1); a_5 and a_8 a_n=(n-1)(2-n)(3+n); a_1,a_2,a_3 a_n=(-1)^nn ; a_3,a_5, a_8

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_4 are in HP , then 1/(a_1a_4)sum_(r=1)^3a_r a_(r+1) is root of :

If a_(1)+a_(5)+a_(10)+a_(15)+a_(20)=225 , then the sum of the first 24 terms of the arithmetic progression a_(1), a_(2), a_(3)…….. is equal to

Given that sequence of number a _(1), a _(2) , a_(3),……, a _(1005) which satisfy (a_(1))/( a _(1)+ 1) =(a_(2))/(a _(2) +3) = (a _(3))/(a _(3)+5) = …… = (a _(1005))/(a _(1005)+2009) a_1+a_2+a_3.......a_(1005)=2010 find the 21^(st) term of the sequence is equal to :

Given that sequence of number a _(1), a _(2) , a_(3),……, a _(1005) which satisfy (a_(1))/( a _(1)+ 1) =(a_(2))/(a _(2) +3) = (a _(3))/(a _(3)+5) = …… = (a _(1005))/(a _(1005)+2009) a_1+a_2+a_3.......a_(1005)=2010

Statement -1: If a_(1),a_(2),a_(3), . . . . .,a_(n), . . . is an A.P. such that a_(1)+a_(4)+a_(7)+ . . . .+a_(16)=147 , then a_(1)+a_(6)+a_(11)+a_(16)=98 Statement -2: In an A.P., the sum of the terms equidistant from the beginning and the end is always same and is equal to the sum of first and last term.