Solution:

Provided that,

For the 11^th term, a₁₁ = 38

and for the16^th term, a₁₆ = 73

We all know that,

a₁₁ = a+(11−1)d

38 = a+10d —————–(i)

Similarly,

a₁₆ = a +(16−1)d

73 = a+15d —————–(ii)

 (ii) – (i) , we get

35 = 5d

d = 7

From the equation (i), we get,

38 = a+10×(7)

38 − 70 = a

a = −32

a₃₁ = a +(31−1) d

= − 32 + 30 (7)

= − 32 + 210

= 178

As a result, 31^st term is 178.