Answer:
12 (-0.25)ⁿ
Explanation:
recall that the general form for each term in the geometric progression is
arⁿ
such that the geometric progression looks something like.
ar⁰, ar¹, ar², ar³, ....., arⁿ, ......
also note that r⁰ = 1, hence ar⁰ is simply a
hence the G.P can be written
a, ar, ar², ar³, ....., arⁿ, ......
also note that r can be obtained by simply dividing the 2nd term with the 1stterm. i.e
r = ar ÷ a
now we are given the first 3 terms in the GP as
12, -3, 3/4, ....
comparing with the GP in the previous paragraph, we can see that ,
a = first term = 12
also
r = 2nd term ÷ 1st term
= -3 ÷ 12
= -0.25
hence the nth term
= arⁿ
= 12 (-0.25)ⁿ