Question

If 6 th term of AP is zero prove that the 30 th term of the AP three times of 14 th term

Answer 1

here is the solution.

Answer 2

6th term = a + 5d = 0
So,
(a = -5d) _____ (1)

Now,
30th term = a + 29d
&
14th term = a + 13d

Question says that to prove 30th term is 3 times of 14th term.

So,

14th term × 3 = 30th term
(a + 13d) × 3 = a + 29d
3a + 39d = a + 29d

Now,
putting the value of a from eqn. (1)

3*-5d + 39d = -5d + 29d
-15d + 39d = -5d + 29d
24d = 24d
LHS = RHS

Hence proved.

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