If `(.^(n)C_(r-1))/(a)=(.^(n)C_(r))/(b)=(.^(n)C_(r+1))/(c)`
`n=(ab+2ac+bc)/(b^(2)-ac)andr=(a(b+c))/(b^(2)-ac)`.

If (.^(n)P_(r-1))/(a)=(.^(n)P_(r))/(b)=(.^(n)P_(r+1))/(c) prove that , b^(2)=a(b+c)

If (nP_(r-1))/a=(nP_r)/b=(nP_(r+1))/c then show that b^2-ab-ac=0

If n_(p_(r-1))/a=n_(p_r)/b=n_(p_(r+1))/c ,then show that b^2=a(b+c)

If the coefficients of three successive terms in the expansion of (1+x)^(n) be a ,b and c respectively , then show that , n=(2ac+b(a+c))/(b^(2)-ac)and(a(b+c))/(b^(2)-ac)= no. of the terms has coefficients a .

(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ac)

If (a^(2)-bc)/(a^(2) +bc) + (b^(2)-ac)/(b^(2) + ac) + (c^(2)-ab)/(c^(2)+ab)= 1 then find (a^(2))/(a^(2) + bc) + (b^(2))/(b^(2) + ac) + (c^(2))/(c^(2) +ab)= ?

1.If the coefficients of three successive terms in the expansionof (1+x)^(n) be a,b and c respectively,then show that,n=(2ac+b(a+c))/(b^(2)-ac) and (a(b+c))/(b^(2)-ac) th term has coefficient a

Match the following {:("List-I","List-II"),((I)""^(n)C_(r+1)+2""^(n)C_(r)+""^(n)C_(r-1),(a)""^((n+2))C_(r+1)),((II)""^((n+1))C_(3)-""^(n-1)C_(3),(b)(n-1)^(2)),((III)""^(2n)C_(2)-2""^(n)C_(2),(c)n^(2)),(,(d)""^(n+1)C_(r+1)):} The correct match is

|(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ac,bc,c^(2)+1)|=

If a,b, and c are in H.P.then th value of ((ac+ab-bc)(ab+bc-ac))/((abc)^(2)) is ((a+c)(3a-c))/(4a^(2)c^(2)) b.(2)/(bc)-(1)/(b^(2)) c.(2)/(bc)-(1)/(a^(2)) d.((a-c)(3a+c))/(4a^(2)c^(2))