Question

What is the ninth term of the geometric sequence?4, 12, 36, 108,...

Answer 1

Remember that in a Geometric Sequence each term is found by multiplying the previous term by a constant.

In general, we write a geometric secuence as:

`a,ar,ar^2,ar^3\ldots`

Where:

• a, is the first term of the sequence

,

• r ,is the common ratio (the factor between the terms)

For the particular sequence we're given, notice that we start at 4 and multiply by 3 in each step. This way,

`\begin{gathered} a=4 \\ r=3 \end{gathered}`

Therefore, the formula to calculate the value of the n-th step of the sequence is:

`4\cdot3^(n-1)`

For the ninth term (n = 9):

`\begin{gathered} 4\cdot3^(9-1) \\ \rightarrow4\cdot3^8 \\ \Rightarrow26244 \end{gathered}`

This way, the nith term of the geometric sequence is 26244