Question

Identify the 8th term of the geometric sequence -2, -12, -72 ...

Answer 1

-2 times 6 is -12 times 6 is -72 times 6 is....
just keep multiplying by 6 until you get the eight term.
or save time by just multiplying -2 by 6^7

Answer 2

notice the common ratio is 6, thus \(\bf \Large a_n = a_1 \times r^{n-1}\)
n = nth term
1 = 1st term
r = common ratio

Answer 3

\[\large a_n = a_1r^{n-1}\]using this formula,first figure out the r (ratio). Divide the preceding number by the first number, \(\large \frac{-12}{-2}= 6 \ ...\frac{-72}{-12}=6\) so we know our r= 6. Our n is the # of terms we are trying to find, that is the 8th term. n=8

Plugging this into our formula, we will have \(\large a_8 = (-2)(6)^{8-1}\)

Answer 4

\[\large a_8 = (-2)(6^{7}) = \ ?\]