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If the 3rd and the 9^(t h) terms of an A...

If the 3rd and the `9^(t h)` terms of an AP are 4 and `"\ "8` respectively, which term of this AP is zero?

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Let the first term and the common difference of the A.P. be 'a' and 'd' respectively.
Given that `a_(3)=4 ...(1)`
`rArr a+2d=4`
and `a_(9)=-8 ...(2)`
`rArr a+8d=-8`
Subtract equation (1) from equation (2), we get
`{:(" "a+8d=-8),(underset(-)" "aunderset(-)+2d=underset(-)4),(bar(" "6d=-12" ")),():}`
`rArr d=-2`
put d=-2 in equation (1), we get
a+2(-2)=4
`rArr a=8`
Let `a_(n)=0`
`rArr 8+(n-1)(-2)=0`
`rArr (n-1)(-2)=-8`
`rArr n-1=4 rArr n=5`
`:.` 5th term of the given A.P. is zero.
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