If a1- a2- a3- a4- a5 are in A-P- with common difference - 0- then find the value of -i-15ai- when a3-2-

As a_1, a_2, a_3, a_4, a_5 are in A.P., we have a_1+a_5=a_2+a_4=2a_3. Hence ∑_i=1^5=10. ...

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Sum of n Terms

If a1, a2, ...

Question

If $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}$ are in A.P. with common difference $\neq 0,$ then find the value of $\sum_{i = 1}^{5} a_{i},$ when $a_{3} = 2.$

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

a_{1} = 0

d \neq 0

\frac{a_{3} - a_{2}}{a_{2}} + \frac{a_{4} - a_{2}}{a_{3}} + \frac{a_{5} - a_{2}}{a_{4}} . . . . . . . . . . . . \frac{a_{n} - a_{2}}{a_{n - 1}}

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}, a_{5}

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

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

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}

a_{2}

a_{3}

a_{4}

a_{3}

a_{4}

a_{5}

a_{1}

a_{3}

a_{5}

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