A 1 -5- a 4 -9 1 2 find a 2 - a 3

a_1 = 5 a_4 = 91/2 a + 3d = 19/2 5 + 3d = 19/3 3d = 19/2 5 3d = 9/2 d = 3/2 so, a_2 = a + d = 5 + 3/2 = 13/2 = 61/2 ...

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Sequence

a 1 =5; a 4 =...

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$a_{1} = 5; a_{4} = 9 \frac{1}{2}$ find $a_{2}, a_{3}$

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A P s

a_{1} = 5, a_{4} = 9 \frac{1}{2}

a_{2}, a_{3}

a_{1}, a_{2}, a_{3}, a_{4}, a_{5} > 0

\frac{a_{1}}{a_{2} + a_{3}} + \frac{a_{2}}{a_{3} + a_{4}} + \frac{a_{3}}{a_{4} + a_{5}} + \frac{a_{4}}{a_{5} + a_{1}} + \frac{a_{5}}{a_{1} + a_{2}} \geq \frac{5}{2}

a_{1}, a_{2}, a_{3}, a_{4}

\frac{a_{2} a_{3}}{a_{1} a_{4}} = \frac{a_{2} + a_{3}}{a_{1} + a_{4}} = 3 (\frac{a_{2} - a_{3}}{a_{1} - a_{4}})

a_{1}

a_{2}

a_{3}

a_{4}

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