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The progression is : 2,5,8,11,14,17

The 7th term of an AP is four times its 2nd term

12th term is two more than three times of its 4 th term.

The progression.

First term of an AP =a

Common difference=d

Tn = n th term

a = First term

n = Number of terms

d = Common difference

The 7th term of an AP is Four times its 2nd term.

⟹T₇ = 4 T₂

⟹a + (7 - 1) d = 4 { a +(2 - 1)d}

⟹a + 6d = 4 {a + d}

⟹4a - a = 6d - 4d

⟹3a = 2d_________(i)

12th term is 2 more than three times of its 4 th term.

⟹T₁₂=3T₄+2

⟹a + (12 - 1) d = 3{a +(4 - 1)d}+2

⟹a + 11d = 3{a + 3d} + 2

⟹a + 11d = 3a + 9d + 2

⟹11d - 9d = 3a - a + 2

⟹2d = 2a + 2

⠀⠀⠀[From eqⁿ (i) 2d = 3a]

⟹3a = 2a + 2

⟹3a - 2a = 2

First term = 2

In equation (i)

⟹2d = 3a

⟹2d = 3×2

⠀⠀⠀⠀⠀[The value of a=2]

⟹2d = 6

⟹d = 3

Common difference = 3

⟹T₁ = a = 2

⟹T₂ = a + d = 2 + 3 = 5

⟹T₃ = a + 2d = 2 + 6 = 8

⟹T₄ = a + 3d = 2 + 9 = 11

⟹T₅ = a + 4d = 2 + 12 = 14

⟹T₆ = a + 5d = 2 + 15 = 17

oof

step-by-step explanation:

one peck is 9.309 quarts

9.309x 2