Question

please .............................. help me

Answer 1

Answer :

Let the 1st term of the AP is a and the common difference is d

We know that n-th term is

aₙ = a + (n - 1)d

Then, a₁ = a

a₂ = a + d

a₃ = a + 2d

a₄ = a + 3d

a₅ = a + 4d

a₆ = a + 5d

a₇ = a + 6d

a₈ = a + 7d

Given that,

a₃ + a₅ + a₈ = 11

⇒ a + 2d + a + 4d + a + 7d = 11

⇒ 3a + 13d = 11 ...(i)

a₄ + a₂ = - 2

⇒ a + 3d + a + d = - 2

⇒ 2a + 4d = - 2

⇒ 3 (2a + 4d) = 3 (- 2)

⇒ 2 (3a) + 12d = - 6

⇒ 2 (11 - 13d) + 12d = - 6, by (i)

⇒ 22 - 26d + 12d = - 6

⇒ 14d = 28

⇒ d = 2

Now, putting d = 2 in (i), we get

3a + 13 (2) = 11

⇒ 3a = 11 - 26

⇒ 3a = - 15

⇒ a = - 5

∴ a₁ + a₆ + a₇

= a + a + 5d + a + 6d

= 3a + 11d

= 3 (- 5) + 11 (2)

= - 15 + 22

= 7 [ option (c) is correct ]

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