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If the 9th term of an AP is zero, then p...

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

Text Solution

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Let the first term and the common difference of the A.P. be 'a' and 'd' respectively.
Given that, `a_(9)=0`
`rArr a+8d=0`
`rArr a=-8d " " ...(1)`
Now, `a_(29)=a+28d=-8d+28d " "` [from (1)]
`=20d`
and `T_(19)=a+18d=-8d+18d " "`[from (1)]
`=10d`
`rArr 2T_(19)=20d`
`:. T_(29)=2T_(19) " " ` Hence Proved.
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