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Arithmetic Progressions

Question
CBSEENMA10007969

If 9th term of an A .P. is zero. Prove that 29th term is double of its 19th term. 

Solution

 Let a be the first term and d be the common difference of the A .P. we have,
a9 = 0 ⇒ a + 8d = 0 ⇒ a = – 8d
Now, a29 = a + 28d = –8d + 28d = 20d
2(a19) = 2(a + 18d) = 2(– 8d + 18d)
= 2(10d) = 20d
Hence, a29 = 2 (a19)