Question

What is the 9th term of the geometric sequence 4, -20, 100, ...?

Answer 1

you need to find the common ratio

to do this compare the terms

\[\frac{T_{2}}{T_{1}} = \frac{T_{3}}{T_{2}}... or ... \frac{-20}{4} = \frac{100}{-20}.. so .. r = ?\]

then the formula for a term in a geometric sequence is

\[T_{n} = ar^{n -1}\]

n = number of terms ( in your question its 9)
a = 1st term ( in your question its 4)
r = common ratio which you found above.

hope this helps

Answer 2

thank you