The difference between the first term and the second term in a geometric sequence is 6. The difference between the second term and the third term is 3. Calculate the difference between the third term and the fourth term.

Question

Thanks to anyone who helps

Answer 1

Let's just translate into Math:
"The difference between the first term and the second term in a geometric sequence is 6" -----> ar - a = 6
a(r-1) = 6 **
"The difference between the second term and the third term is 3. "
----> ar^2 - ar = 3
ar(r-1) = 3 ***
divide *** by **
ar(r-1) / (a(r-1)) = 3/6
r = 1/2
sub back into **
a(1/2-1) = 6
a = -12

the difference between the third term and the fourth term
= ar^3 - ar^2
= ar^2(r-1)
= -12(1/4)(-1/2) = 3/2

check: the sequence is -12, -6, -3, -3/2
find the differences as stated and you will see my answer is correct