Question

The 6 term of an AP is zero prove that the 21 term is tripled its 11 term ​

Answer 1

ANSWER:

GIVEN:

• 6th term of an A.P = 0

TO PROVE:

• 21 term is tripled of its 11 term .

SOLUTION:

Formula:

=> nth term = a+(n-1)d

Where:

=> a = first term

=> n = number of terms.

=> d = common difference.

Let an A.P whose first term = a and common difference is d.

=> 6th term = a+(6-1)d

=> 0 = a+5d

=> a = (-5d) .....(i)

=> 21st term = a+(21-1)d

=> 21st term = a+20d

Putting a = (-5d) from eq(i)

=> 21st term = (-5d)+20d

=> 21st term = 15d ....(ii)

=> 11th term = a+(11-1)d

=> 11th term = a+10d

Putting a = (-5d) from eq(i)

=> 11th term = (-5d)+10d

=> 11th term = 5d ....(iii)

Now

=> 15d = 3(5d)

=> 21st term = 3(11th term). [from eq(ii) ad (iii)

Proved.