Find a GP. for which sum of first two terms is –4 and fifth term is 4 times the 3rd term.

Let the G.P. be a, ar, ar², ..........
Given          a + ar = -4                                                                        ...(i)
Also,             
or                
                                                                              (∵ )
                         
Putting r = 2 in (i), we get a + 2a = -4  a = -4/3.
∴    G.P. is 
Now, putting r = -2 in (i), we get a + a(-2) = -4  -a = -4 or a = 4.
∴  G.P. is 4, 4(-2), 4(-2)²,   .... or 4, -8, 16, ...........