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The correct Answer is:
9
Given, `(S_(7))/(S_(11)) = (6)/(11) and 130 lt t_(7) lt 140`
`rArr ((7)/(2)[2a + 6d])/((11)/(2) [2a + 10d]) = (6)/(11) rArr (7 (2a + 6d))/((2a + 10d))= 6`
`rArr a = 9d`..(i)
Also, `130 lt t_(7) lt 140`
`rArr 130 lt a + 6d lt 140`
`rArr 130 lt 9d + 6d lt 140` [from Eq. (i)]
`rArr 130 lt 15d lt 140`
`rArr (26)/(3) lt d lt (28)/(3)` [since, d is a natural number]
`:. d = 9`
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