In the following A.P., find the missing terms:

□, □, 13, □, □, 22

Given: a₃ = 13 and a₆ = 22

We know that,

a_n = a + (n – 1)d

a₃ = a + (3 – 1)d

13 = a + 2d …(i)

and a₆ = a +(6 – 1)d

22 = a + 5d …(ii)

Solving linear equations (i) and (ii), we get

a + 2d – a – 5d = 13 – 22

⇒ –3d = 9

⇒ d = 3

Putting the value of d in eq. (i), we get

a + 2(3) = 13

⇒ a + 6 = 13

⇒ a = 7

Now, a₂ = a + d = 7 + 3 = 10

a₄ = a + 3d = 7 + 3(3) = 7 + 9 = 16

a₅ = a + 4d = 7 + 4(3) = 7 + 12 = 19

Hence, the missing terms are 7, 10, 16 and 19