Find a G.P. for which sum of the first two terms is \( -4 \) and the fifth term is \( 4 \) times the third term.

Given \( a + ar = -4 \) and \( ar^4 = 4ar^2 \implies r^2 = 4 \implies r = \pm 2 \). If \( r = 2 \), \( a = -\frac{4}{3} \) (not integer); if \( r = -2 \), \( a(1 - 2) = -4 \implies a = 4 \), giving terms \( 4, -8, 16 \dots \) wait: check \( a+ar = 4 - 8 = -4 \), \( r = -2 \). Terms are \( 4, -8, 16 \dots \)