Arithmetic and Geometric Seque

Let a - d , a , a + d be three consecutive terms , then

(a - d) + a + (a + d) = - 3
3a = - 3
a = - 1

and

(a - d) a (a + d) = 15
(- 1 - d) (- 1) (- 1 + d) = 15
(d + 1) (d - 1) = 15
d² - 1 = 15
d = 4 or - 4

Therefore the three terms are :

- 1 - 4 , - 1 , - 1 + 4
i.e.
- 5 , - 1 , 3

or

- 1 - (-4) , - 1 , - 1 + (-4)
i.e.
3 , - 1 , - 5