Question

The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is ______.

Options

• 2

• 3

• `3/2`

• –1

Answer 1

The fourth term of an A.P. is three times of the first term and the seventh term exceeds the twice of the third term by one, then the common difference of the progression is 2.

Explanation:

Let the progression be a, a + d, a + 2d,

Then x₄ = 3x₁ `\implies` a + 3d = 3a `\implies` 3d = 2a  ...(i)

Again x₇ = 2x₃ + 1

`\implies` a + 6d = 2(a + 2d) + 1 `\implies` 2d = a + 1  ...(ii)

Solving (i) and (ii) we get

2d = `(3d)/2 + 1 \implies` 4d = 3d + 2 `\implies` d = 2

3(2) = 2a `\implies` a = 2

a = 3, d = 2