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given: a3=15,S[10]=125, find d and a[10]...

given: `a_3=15`,`S_[10]=125`, find d and `a_[10]`

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Let first term be 'a'.
`a_(3)=15`
`rArr a+2d=15`
`S_(10)=125 " " ...(1)`
`rArr (10)/(2)(2a+9d)=125`
`rArr 5[2(15-2d)+9d]=125 " " ` [from (1)]
`rArr 30-4d+9d=25`
`rArr 5d=-5 rArr d=-1`
put d=-1 in equation (1)
`a+2(-1)=15 rArr a=17`
`:. a_(10)=a+9d=17+9(-1)=8`
Hence, d=-1 and `a_(10)=8`
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