Let a1,a2 be first two terms and a3,a5 be third and fifth terms respectively.
according to question
a1+a2 = – 4 ⇒ a + ar = – 4 ⇒ a(1 + r) = – 4 ....(i)
and a5 = 4a3 ⇒ ar4 = 4ar2 ⇒ r2 = 4 ⇒ r = ± 2
If r = 2, then (i) becomes a(1 + 2) = – 4 ⇒a =
If r = – 2, then (i) becomes a (1 – 2) = – 4 ⇒ a = 4
When a = −

4

3

and r = 2, then G.P. is −

4

3

,−

8

3

,−

16

3

, ...
When a = 4 and r = – 2, then G.P. is 4, – 8, 16, – 32, ........ .