If a 1- a 2- a 3- a 4- - are in A-P- and a 1- a 5- a 9- a 29-64- then the value of a 3- a 8- a 22- a 27 is

A_1+a_5+a_9+ ...+a_29=64 ⇒ (a_1+a_29)+(a_5+a_25)+(a_9+a_21)+(a_13+a_17)=64 ⇒ 4k=64 ⇒ k=16 a_3+a_8+a_22+ a_27 =(a_3+ a_27)+(a_8+a_22) =2k=32 ...

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If $a_{1}, a_{2}, a_{3}, a_{4}, \dots$ are in A.P. and $a_{1} + a_{5} + a_{9} + . . . + a_{29} = 64$ , then the value of $a_{3} + a_{8} + a_{22} + a_{27}$ is

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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}, \dots \dots

a_{3} + a_{5} + a_{8} = 11

a_{4} + a_{2} = - 2

a_{1} + a_{6} + a_{7}

A . P .

a_{1}, a_{2}, a_{3}, . . . . . ., a_{n}, . . . . .

a_{1} + a_{3} + a_{5} = - 12

a_{1} a_{2} a_{3} = 8

a_{2} + a_{4} + a_{6}

a_{1}, a_{2}, a_{3}, \dots

a_{3} + a_{5} + a_{8} = 11

a_{4} + a_{2} = - 2

a_{1} + a_{6} + a_{7}

a_{1}

a_{2}

a_{3}

a_{2}

a_{3}

a_{4}

a_{3}

a_{4}

a_{5}

a_{1}

a_{3}

a_{5}

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