The fourth ,sixth,ninth terms of AP forms first three terms of GP if first three of AP is 3 find common difference

Answer 1

Let the fourth term of the AP be a, the sixth term be c, and the ninth term be e.

Since the first three terms of the AP are 3, the second term (a1) is 3 - d, the third term (a2) is 3 - 2d, and the fourth term (a3) is 3 - 3d.

We know that a3 = a + 3d, so 3 - 3d = 3 + 3d.
Simplifying this equation, we get -6d = 0, so d = 0.

Therefore, the common difference of the AP is 0.