Question

The fourth term of an arithmetic

progression is one less than twice the
second term If the sixth term is 7,
find the first term​

Answer 1

2

Explanation:

Given AP where:

• a₄ = 2a₂ - 1
• a₆ = 7

To find

• a₁ = ?

Since

• a₄ = a₁ + 3d
• a₂ = a₁ + d
• a₆ = a₁ + 5d

Initial equations will change as:

• a₁ + 3d = 2(a₁ + d) - 1 ⇒ a₁ + 3d = 2a₁ + 2d - 1 ⇒ a₁ = d + 1
• a₁ + 5d = 7 ⇒ a₁ = 7 - 5d

Comparing the above:

• d + 1 = 7 - 5d
• 6d = 6
• d = 1

Then:

• a₁ = d + 1 = 1 + 1 = 2
• a₁ = 2

The first term is 2