Question

determine third term in the geometric sequence whose first term is -8 and whose common ratio is 6

Answer 1

use the n'th term formula
\(\Large a_n = a_1 r^{n-1}\)

a1 = 1st term = -8
r = common ratio = 6

Answer 2

Or simply write the first term (-8) and label it as such.
Multiply this first term by the common ratio (6).
What do you get? If correct, this is your second term.

Show your work, please.

Answer 3

−48

Answer 4

@mathman101

Answer 5

OK: Your first term is -8 (given), and your common ratio is 6 (also given). You've multiplied your first term by the common ratio and thus obtained your second term (-48). Now multiply your second term by the common ratio. That's how you arrive at your third term. There's a formula for this, but this first, simple approach shows you what's happening here.