Question

8 times of the eight term of an arithmetic progression is equal to 12 times of the twelfth term. find its first term if the common difference is -2 .​

Answer 1

a₁ = 38

Explanation:

Given AP, where:

• 8a₈ = 12a₁₂
• d = -2,
• a₁ = ?

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Solution

aₙ = a₁ + (n-1)d

• a₈ = a₁ + 7d = a₁ + 7*(-2) = a₁ - 14
• a₁₂ = a₁ + 11d = a₁ + 11*(-2) = a₁ - 22

8a₈ = 12a₁₂

• 8(a₁ - 14) = 12(a₁ - 22)
• 2(a₁ - 14) = 3(a₁ - 22)
• 2a₁ - 28 = 3a₁ - 66
• 3a₁ - 2a₁ = -28 + 66
• a₁ = 38