13. If 6 times the 6th term of an A. P. is equal to 13 times the 13th term, prove that 19th term
of this A. P. is zero.

please give the answer as fast as you can

please

see explanation

Step-by-step explanation:

The n th term of an AP is

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given

6(a₁ + 5d) = 13(a₁ + 12d) ← distribute parenthesis on both sides

6a₁ + 30d = 13a₁ + 156d ( subtract 13a₁ from both sides )

- 7a₁ + 30d = 156d ( subtract 30d from both sides )

- 7a₁ = 126d ( divide both sides by - 7 )

a₁ = - 18d

Now

a₁₉ = a₁ + 18d = - 18d + 18d = 0 ← as required

step-by-step explanation:

the true ones are a b and d