Question

if the 9th term of A.p.is zero then prove that the 29th term is double of 19th term
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Answer 1

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Answer 2

We know that nth term of an AP(an) = a + (n - 1) * d.

Given that 9th term of an AP is zero.

⇒ a9 = a + (9 - 1) * d

⇒ 0 = a + 8d    

⇒ a = -8d ------ (1)

Then, 29th term of an AP a29 = a + (29 - 1) * d

⇒ a + 28d

⇒ -8d + 28d

⇒ 20d.

Then, 19th term of An AP a19 = a + (19 - 1) * d

⇒ a + 18d

⇒ -8d + 18d

⇒ 10d.

Therefore,

From the above calculations.. we can say that:

⇒ 29th term is double of 19th term.

⇒ a29 = 2 * (a19).

Hope this helps!