Find missing term in arithmetic progression

Let ‘a’ is the first term, ‘d’ is a common difference then the general term of an AP is given by the formula AP = a + (n – 1)d. Now, given terms are 11th and 16th.
By Using the general term, 11th term of an AP = 38
⇒ a + (11 – 1)d = 38
⇒ a + 10d = 38 ———————— (1)
16 th term of an AP = 73
⇒ a + (16 -1)d = 73
⇒ a + 15d = 73 ———————— (2)
By solving both the equations by subtracting equation (1) from (2) we will get the result. i.e.
⇒ (a + 15d) – (a + 10d) = 73 – 38
⇒ a + 15d – a – 10d = 35
⇒ 15d – 10d = 35
⇒ 5d = 35 (Dividing by 5 both sides
∴ d = 7
Put the value of d in any of the equation 1 or 2. Substitute value of d = 7 in equation (1)
⇒ a + 10 × 7 = 38
⇒ a + 70= 38
⇒ a = 38 – 70
∴ a = – 32
Now,
∴ 31st term of an AP = -32 + (31 – 1)×7 = -32 + 30×7 = 178
Answer: 31st Term is 178