What are the missing numbers in the given A.P.?

?,13,?,3

It is given that,

a₂ = 13 and a₄ = 3

As we know, for an A.P.,

a_n = a + (n−1) d

Therefore, putting the values here,

a₂ = a  + (2-1) d

13 = a + d ………………. (i)

a₄ = a + (4-1) d

3 = a + 3d ………….. (ii)

On subtracting equation (i) from (ii), we get,

–10 = 2d

d = – 5

From equation (i), putting the value of d, we get

13 = a + (-5)

a = 18

a₃ = 18 + (3-1)(-5)

= 18 + 2(-5) 

= 18 - 10 

= 8