Q12 of 38 Page 5

If the 9th term of an AP is zero, then prove that its 29th term is twice its 19th term.

Given: a9 = 0


To prove: a29 = 2a19


Formula Used: nth term of an AP is:


an = a + (n - 1) d


Proof:


As a9 = 0


⇒ a + 8d = 0 [ eqn i]


Using the nth term formula i.e. an = a + (n - 1) d


Taking LHS


a29 = a + 28d


= (2 - 1) a + (36 - 8) d


= 2a - a + 36d - 8d


= 2a + 36d - (a + 8d )


= 2(a + 18d) - 0 [ using i]


= 2a19 [as a9 = a + 8d]


= RHS


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