Question

If the sum of first 11 terms of an AP.,
a1,a2 ,... is 0 (a1 not equals to 0), then the sum of the AP.,
a1, a3, a5 ,..., a23 is ka1, where k is equal to?
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Answer 1

Heya ,

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a₁ + a₂ + a₃ + ____ + a₁₁ = 0

⇨( a₁ + a₁₁ ) x 11/2 = 0

⇨a₁ + a₁₁ = 0

⇨a₁ + a₁ + 10d = 0

Here , d is common difference -

⇨a₁ = -5d

a₁ + a₃ + a₅ + ___ + a₂₃

= ( a₁ + a₂₃ ) x 12/2 = ( a₁ + a₁ + 22d ) x 6

= 〈 2a₁ + 22 [ -a₁ /5] 〉 x 6

= -72/5 a₁ ⇨K = -72/5

ʜᴇɴᴄᴇ ᴛʜᴇ ʀᴇǫᴜɪʀᴇᴅ ᴀɴsᴡᴇʀ ɪs -72/5

Fᴏʀ ᴍᴏʀᴇ :

If the sum of first 11 terms of an AP.,

a1,a2 ,... is 0 (a1 not equals to 0), then the sum of the AP.,

a1, a3, a5 ,..., ...

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Answer 2

Answer:

a₁ + a₂ + a₃ + ____ + a₁₁ = 0

⇨( a₁ + a₁₁ ) x 11/2 = 0

⇨a₁ + a₁₁ = 0

⇨a₁ + a₁ + 10d = 0

Here , d is common difference -

⇨a₁ = -5d

a₁ + a₃ + a₅ + ___ + a₂₃

= ( a₁ + a₂₃ ) x 12/2 = ( a₁ + a₁ + 22d ) x 6

= 〈 2a₁ + 22 [ -a₁ /5] 〉 x 6

= -72/5 a₁ ⇨K = -72/5

ʜᴇɴᴄᴇ ᴛʜᴇ ʀᴇǫᴜɪʀᴇᴅ ᴀɴsᴡᴇʀ ɪs -72/5

Fᴏʀ ᴍᴏʀᴇ :

If the sum of first 11 terms of an AP.,

a1,a2 ,... is 0 (a1 not equals to 0), then the sum of the AP.,

a1, a3, a5 ,..., ...