Question

Find the value of ‘x’ if x + 1, 2x + 1, and x + 7 are in A.P. Also, find the 4th term of this progression.

Answer 1

In an Arithmetic Progression (AP), the difference between consecutive terms is constant. If a, b, c are in AP, then:

2b = a + c

Substitute the given terms a = x + 1, b = 2x + 1, and c = x + 7:

2(2x + 1) = (x + 1) + (x + 7)

4x + 2 = 2x + 8

2x = 6

x = 3

Wait, let’s re-verify the calculation:

4x − 2x = 8 − 2

⇒ 2x = 6

⇒ x = 3

a₁ = 3 + 1 = 4

a₂ = 2(3) + 1 = 7

a₃ = 3 + 7 = 10

The common difference (d) = 7 − 4 = 3

a₄ = a₃ + d

a₄ = 10 + 3

a₄ = 13