Question

if the 9th term of an A.P is 0 prove that it's 29th term is twice it's 19 term
give answer with full explanation with steps .
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Answer 1

$a + 8d = 0$

$a = - 8d$

$so \: \: \: \: 19th \: term = a + 18d$

$- 8d + 18d = 19th \: term$

$19th \: term \: = 10d...................(i)$

$29th \: term \: = a + 28d$

$= - 8d + 28d$

$29th \: term \: = 20d..............(ii)$

$we \: can \: clearly \: see \: equations \: (i) \: and \: (ii) \: that \: the \: 29th \: term \: is \: twice \: the \: 19th \: term$