the third and the sixth term of a G.p are 5 and -40 respectively. find the tenth term of the sequence?

Answer 1

using the definitions of a GP

ar^2 = 5
ar^5 = -40
divide the second by the first
r^3 = -8
r = -2

back in the first:
ar^2 = 5 ---> a(4) = 5
a = 5/4

term(10) = ar^9
= (5/4)(-2)^9
= (5/4)(512)
= -640