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If a(1),a(2),a(3),a(4) and a(5) are in A...

If `a_(1),a_(2),a_(3),a_(4)` and `a_(5)` are in AP with common difference `ne 0,` find the value of `sum_(i=1)^(5)a_(i) " when " a_(3)=2`.

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`therefore a_(1),a_(2),a_(3),a_(4)and a_(5)` are in AP, we have
`a_(1)+a_(5)=a_(2)+a_(4)+ a_(3)+a_(3) " "[thereforet_(n)+t'_(n)=a+l]`
`a_(1)+a_(5)=a_(2)+a_(4)=4" "[therefore a_(3)=2]`
`a_(1)+a_(2)+a_(3)+a_(4)+a_(5)=4+2+4=10`
`implies " "sum_(i=1)^(5)a_(i)=10`
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