QJEEM20Mad1a5: JEE Main 2020 Mathematics - Class 11 JEEM20Mad1a5 Solution: If the sum of first 11 terms of an A.P., a 1 , a 2 , a 3 , .... …

Question

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If the sum of first 11 terms of an A.P.,
a₁, a₂, a₃, .... is 0 (a

\neq

0), then the sum of the A.P.,
a₁ , a₃ , a₅ ,....., a₂₃ is ka₁ , where k is equal to :

Accepted Answer

Let common difference be d.

∵

a₁ + a₂ + a₃ + ... + a₁₁ = 0

∴

\frac{11}{2} [2 a_{1} + 10 d]

= 0

\Rightarrow

a₁ + 5d = 0

\Rightarrow

d =

- \frac{a_{1}}{5}

.....(1)

Now a₁ + a₃ + a₅ + ... + a₂₃

= (a₁ + a₂₃)

\times

\frac{12}{2}

= (a₁ + a₁ + 22d) × 6

=

[2 a_{1} + 22 (- \frac{a_{1}}{5})]

\times

6

=

- \frac{72}{2} a_{1}

∴

k =

- \frac{72}{2}

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