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

Answer:

4,374

Explanation:

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

If we study the pattern we observe that:

$\begin{gathered} \frac{6}{2}=3 \\ \frac{18}{6}=3 \end{gathered}$

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:

$\begin{gathered} U_8=2\times3^{8-1} \\ =2\times3^7 \\ =4374 \end{gathered}$

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