Find the 31st term of an AP (**Arithmetic Progression**) whose 11th term is 38 and 16th term is 73.

1 Answers

**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**

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