Option 4 : 40

**Given:**

The difference between the 6th term and 3rd term of an AP is equal to the second term of the AP.

The sum of the first and the 10th term is 52.

**Formula Used:**

n-th term of an AP = a + (n - 1)d, where a is the first term, n is the total number of terms and d is the common difference.

**Calculation:**

Let the first term and common difference be a and d respectively.

(a + 5d) – (a + 2d) = a + d

⇒ 3d = a + d

⇒ a = 2d ----(1)

Now, a + (a + 9d) = 52

2a + 9d = 52

⇒ 4d + 9d = 52 [Using (1)]

⇒ 13 × d = 52

⇒ d = 4

So, a = 2 × 4 = 8

9th term = a + 8d = 8 + 8 × 4 = 8 + 32 = 40

**∴ 9th term is 40**