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Write the first three terms of the seque...

Write the first three terms of the sequence defined by `a_1 2,a_(n+1)=(2a_n+3)/(a_n+2)` .

Text Solution

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Put
`n=1` in `a_(n+1)=(2a_(n)+3)/(a_(n)+2)`, we have
`a_(1+1)=a_(2)=(2a_(1)+3)/(a_(1)+2)=(2(2)+3)/((2)+2)=7/4`
Put n=2, then we have `a_(2+1)=a_(3)=(2a_(2)+3)/(a_(2)+2)`
`=(2(7/4)+3)/((7/4)+2)=26/15` ltbr gtSo, first three terms are 2,`7/4,26/15`
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