Question

the sum of the 4th and 8th term of an AP is 24 and the sum of the 6th and 10th term is 34. Find the first four terms of an AP.​

Answer 1

Step-by-step explanation:

a4 + a8 = 24

==> a + 3d + a + 7d = 24

==> 2a + 10d = 24

==> a + 5d = 12

==> a = 12 - 5d ------- eq 1

a6 + a10 = 34

==> a + 5d + a + 9d = 34

==> 2a + 14d = 34

==> a + 7d = 17 ------- eq 2

Substituting the eq1 in eq 2.

==> 12 - 5d + 7d = 17

==> 2d = 5

d = 5/2

put value of d=2.5 in eq(1) we get

a1 = −1/2 = -0.5 =  first term of A.P

Answer 2

GivEn:

• Sum of 4ᵗʰ and 8ᵗʰ term of an AP is 24.
• Sum of 6ᵗʰ and 10ᵗʰ term of an AP is 34.

To find:

• First four term of an AP

SoluTion:

★ a₄ + a₈ = 24

⇏(a + 3d) + (a + 7d) = 24

⇏ 2a + 10d = 24⠀⠀⠀⠀⠀⠀⠀eq. (1)

★ a₆ + a₁₀ = 34

⇏ (a + 5d) + (a + 9d) = 34

⇏ 2a + 14d = 34⠀⠀⠀⠀⠀⠀⠀eq. (2)

Now, subtracting eq (2) from eq (1),

⇏ 2a + 10d - (2a + 14d) = 24 - 34

⇏2a + 10d - 2a - 14d = - 10

⇏- 4d = - 10

⇏d = - 10/ - 4

⇏d = 2.5

★ Now, Putting value of d in eq (1),

⇏ 2a + 10(2.5) = 24

⇏2a + 25 = 24

⇏2a = 24 - 25

⇏2a = - 1

⇏a = -1/2

⇏ a = - 0.5

∴ Hence, First term and common difference of AP is - 0.5 and 2.5 respectively.

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Therefore,

First four term of AP are,

• a₁ = - 0.5

• a₂ = a + d = - 0.5 + 2.5 = 2

• a₃ = a + 2d = - 0.5 + 2 × 2.5 = 4.5

• a₄ = a + 3d = - 0.5 + 3 × 2.5 = 7