Determine the AP whose 3rd term is 5 and the 7th term is 9

• Arithmetic Progression (C10)

Determine the AP whose 3rd term is 5 and the 7th term is 9.

Solution

a₃ = a + (3 – 1)d = a + 2d = 5 ... (1)

a₇ = a + (7 – 1)d = a + 6d = 9 ... (2)

Solving the pair of linear equations (1) and (2),

a = 3, d = 1

Hence, the required AP is 3, 4, 5, 6, 7, ...