Find the common difference (d) by subtracting the 11th term from the 16th term and dividing by the number of terms between them.

Which formula use to find the 31st term of the AP.

How it is expresses the nth term an in terms of the first term a1 and the common difference.

Class 10th Maths, Important Arithmetic Progression Solutions.

# Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

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Here, a₁₁ = 38 and a₁₆ = 73. To find: a₃₁

Given that: a₁₁ = a + (11 – 1)d = 38

⇒ a + 10d = 38

⇒ a = 38 – 10d ….(1)

and a₁₆ = 73 ⇒ a + 15d = 73

Putting the value of a from equation (1), we get

38 – 10d + 15d = 73

⇒ 5d = 35 ⇒ d = 7

Putting the value of d in equation (1), we get

a = 38 – 10(7) = – 32

Therefore, a₃₁ = a + 30d = – 32 + 30(7) = 178

Hence, the 31st term is 178.