Show that each one of the following progressions is a G.P. Also, find the common ratio in each case :

i. 4, -2, 1, ,….

ii.

iii.

iv.

(i) Let a = 4, b = -2, c = 1.

In GP, b²=ac

⇒ (-2)² = 4.1

⇒ 4 = 4

Common ratio = r

(ii) Let , b = -6, c = -54.

In GP, b²=ac

⇒

⇒ 36 = 36

Common ratio = r

(iii) Let a = a,

In GP, b²=ac

⇒

⇒

Common ratio

(iv) Let

In GP, b²=ac

⇒

⇒

Common ratio