Question

IF 9th TERM OF AN AP IS ZERO THEN PROVE THAT ITS 29th TERM WILL BE DOUBLED TO ITS 19th TERM

Answer 1

t9=0
t9 =a +(n-1)d
t9=a+(9-1)d
t9= a+8d
a+8d=0
a=-8d
t29= a+28d
-8d+28d
=20d
t19= a+18d
-8d+18d
=10d
here t19.=10d, t29=20d
on multiplying t19 by 2 we get t29 value
here t29 =20d, which is double of t19

Answer 2

a9= 0
a+ (9-1) d=0
a+8d =0
a=-8d......(I)
to prove: a29 2a19

proof : LHS= a29=a+28d =-8d+28d= 20d
RHS= 2a19= 2[a+(18)d]= 2(-8d+18d)=2(10d)=20d
since, LHS=RHS
hence proved