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in Arithmetic Progression by (56.3k points)

If 9th term of an A.P. is zero, prove its 29th term is double the 19th term.

1 Answer

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Best answer

Given,

a9 = 0

We know that, nth term an = a + (n – 1)d

So, a + (9 – 1)d = 0 ⇒ a + 8d = 0 ……(i)

Now,

29th term is given by a29 = a + (29 – 1)d

⇒ a29 = a + 28d

And, a29 = (a + 8d) + 20d [using (i)]

⇒ a29 = 20d ….. (ii)

Similarly, 19th term is given by a19 = a + (19 – 1)d

⇒ a19 = a + 18d

And, a19 = (a + 8d) + 10d [using (i)]

⇒ a19 = 10d …..(iii)

On comparing (ii) and (iii), it’s clearly seen that

a29 = 2(a19)

Therefore, 29th term is double the 19th term.

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