Question

11th term of an A.P is 0. Show that its 31st term is twice the 21th term.

Answer 1

Answer:

Let 11th of the A.P. is a+10d=0

As a+10d=0, then a= -10d

A.T.Q.

we, need to prove: a+30d= 2(a+20d)

Putting the value of a in both LHS and RHS

putting that we get,

20d= -20d+40d

20d= 20d

LHS=RHS

Hence Proved

Answer 2

Answer:

The 31st is twice the 21st term.

Step-by-step explanation:

given:a(11)=0

to prove:a(31)=2a(21)

sol:

a(11)=a+(n-1)d

   0=a+10d

:.a=-10d

a(21)=a+(n-1)d

      =-10d+20d

      =10d

now,

a(31)=a+(n-1)d

       =-10d+30d

      =20d

a(31)=20d and a(21)=10d

:.:a(31)=2a(21)

HENCE PROVED