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_2,a_3,a_4 are in H.P. then 1/(a_1 a_4) sum_(r=1)^3 a_r a_(r+1) is a root of (A) x^2-2x-15=0 (B) x^2+2x+15=0 (C) x^2+2x-15=0 (D) x^2-2x+15=0

If a_1,a_2,a_3,a_4 are in H.P. then 1/(a_1 a_4) sum_(r=1)^3 a_r a_(r+1) is a root of (A) x^2-2x-15=0 (B) x^2+2x+15=0 (C) x^2+2x-15=0 (D) x^2-2x+15=0

If a_(1),a_(2),a_(3),a_(4) are in HP, then (1)/(a_(1)a_(4))sum_(r=1)^(3)a_(r)a_(r+1) is root of :

Let f:RrarrR such that f(x) is continuous and attains only rational value at all real x and f(3)=4. If a_1,a_2,a_3,a_4,a_5 are in H.P. then sum_(r=1)^4 a_r a_(r+1)= (A) f(3).a_1a_5 (B) f(3).a_4a_5 (C) f(3).a_1a_2 (D) f(2).a_1a_3

Let f:RrarrR such that f(x) is continuous and attains only rational value at all real x and f(3)=4. If a_1,a_2,a_3,a_4,a_5 are in H.P. then sum_(r=1)^4 a_r a_(r+1)= (A) f(3).a_1a_5 (B) f(3).a_4a_5 (C) f(3).a_1a_2 (D) f(3).a_1a_3

"If "a_1,a_2,a_3,.....,a_n" are in AP, prove that "a_(1)+a_(n)=a_(r)+a_(n-r+1)""

If a_1,a_2,a_3...a_n are in HP and f(k)=sum_(r=1)^na_r-a_k, then a_1/(f(1)),a_2/(f(2)),a_3/(f(3)),......a_n/(f(n)) are in

If a_1,a_2,a_3….a_r are in G.P then show that |{:(a_(r+1),a_(r+5),a_(r+9)),(a_(r+7),a_(r+11),a_(r+15)),(a_(r+11),a_(r+7),a_(r+21)):}| is independent of r

If a_1, a_2, a_3 ….. a_n are in AP, then prove that frac(1)(a_1 a_2)+frac(1)(a_2 a_3)+frac(1)(a_3 a_4)+.....+frac(1)(a_(n-1) a_n)=frac(n-1)(a_1 a_n)

If a_1,a_2,a_3…a_n are in H.P and f(k)=(Sigma_(r=1)^(n) a_r)-a_k then a_1/f(1),a_2/f(3),….,a_n/f(n) are in