If 9th term of an A.P is zero prove that it\'s 29th term is double the

1.	If 9th term of an A.P is zero prove that it\'s 29th term is double the 19th term
Answer» We have,a9\xa0= 0{tex}\\Rightarrow{/tex}\xa0a + (9 - 1)d = 0{tex}\\Rightarrow{/tex}\xa0a + 8d = 0{tex}\\Rightarrow{/tex}\xa0a = -8dTo prove: a29 = 2a19Proof:LHS = a29= a + (29 - 1)d= a + 28d= -8d + 28d= 20dRHS = 2a19= 2 a + (19 - 1)d]= 2[ -8d + 18d]= 2\xa0{tex}\\times{/tex}10d= 20d{tex}\\therefore{/tex} LHS = RHSHence, 29th\xa0term is double the 19th term.

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