Question

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 2,6, 18,... Find the 8th term.

Answer 1

4,374

Step-by-step explanation:

Given the sequence: 2, 6, 18, ...

If we study the pattern we observe that:

`\begin{gathered} (6)/(2)=3 \\ (18)/(6)=3 \end{gathered}`

This is a geometric sequence with:

• The first term, a=2

,

• Common Ratio, r=3

The nth term of a geometric sequence is obtained using the formula:

`U_n=ar^(n-1)`

Therefore, the 8th term will be:

`\begin{gathered} U_8=2*3^(8-1) \\ =2*3^7 \\ =4374 \end{gathered}`

The 8th term of the sequence is 4,374.