`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)=1, a_(2)=1, and a_(n)=a_(n-1)+a_(n-2) for n ge 3, find the first 7 terms of the sequence.

If a_(1)=3 and a_(n)=2a_(n-1)+5 , find a_(4) .

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),………. 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) =

Let a_(1), a_(2), a_(3) , … be a G. P. such that a_(1)lt0 , a_(1)+a_(2)=4 and a_(3)+a_(4)=16 . If sum_(i=1)^(9) a_(i) = 4lambda , then lambda is equal to :

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.

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: