AP, GP and HP

If a_n= the digit at units palce in the number o 1!+2!+3!+……….n! for nge4 the a_4, a_5, a_6, ……… are in (A) A.P. only (B) G.P. only (C) A.P. and G.P. only (D) A.P., G.P. and H.P.

If a-b,ax-by,ax^2-by^2a,b!=0) are in G.P., then x,y (ax-by)/(a-b) are in (A) A.P. only (B) G.P.only (C) A.P., G.P. (D) A.P., and G.P and H.P

I a_n= int_0^(pi/2) (1-cos2nx)/(1-cos2x)dx then a_1,a_2,a_3,………,a_n are in (A) A.P. only (B) G.P.only (C) H.P. only (D) A.P., G.P. and H.P.

AP ||GP

If a,b,c are non zero real numbers such that 3(a^2+b^2+c^2+1)=2(a+b+c+ab+bc+ca) then a,b,c are in (A) A.P. only (B) G.P. only (C) A.P., G.P., and H.P. (D) A.P. and G.P.both

If a,b,c are in AP or GP or HP,then (a-b)/(b-c) is equal to

Let the positive numbers a,b,c,d be in AP. Then abc,abd,acd,bcd are (2001,1M) not in AP/GP/HP ( b ) in AP in GP (d) in HP

Let the positive numebrs a,b,c,d be in A.P. Then abc,abd,acd,bcd re (A) not in A.P., G.P., H.P. (B) in A.P. (C) in G.P. (D) in H.P.