Question

The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).
16, comma, 48, comma, 144, comma, dot dot dot
16,48,144,...
Find the 6th term.
Find the 6th term.

Answer 1

To find the 6th term of the sequence 16, 48, 144, we first need to identify the pattern or rule governing the terms.

Let's look at the ratios between consecutive terms:

- From the 1st term (16) to the 2nd term (48):
\[ \frac{48}{16} = 3 \]

- From the 2nd term (48) to the 3rd term (144):
\[ \frac{144}{48} = 3 \]

This shows that each term is multiplied by 3 to get the next term. Therefore, the sequence can be defined as follows:

- 1st term: \( a_1 = 16 \)
- 2nd term: \( a_2 = 16 \times 3 = 48 \)
- 3rd term: \( a_3 = 48 \times 3 = 144 \)
- 4th term: \( a_4 = 144 \times 3 = 432 \)
- 5th term: \( a_5 = 432 \times 3 = 1296 \)
- 6th term: \( a_6 = 1296 \times 3 = 3888 \)

Thus, the 6th term of the sequence is:

\[
\boxed{3888}
\]