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).
11, comma, 22, comma, 44, comma, dot dot dot
11,22,44,...
Find the 7th term.
Find the 7th term.

Answer 1

To determine the 7th term of the sequence given by \(11, 22, 44, \ldots\), we need to identify the pattern in the sequence.

The first three terms are:
- \( a_1 = 11 \)
- \( a_2 = 22 \)
- \( a_3 = 44 \)

We can see that each term in the sequence is multiplied by 2 to obtain the next term:

\[
a_2 = a_1 \times 2 = 11 \times 2 = 22
\]
\[
a_3 = a_2 \times 2 = 22 \times 2 = 44
\]

We can continue this process to find further terms:
\[
a_4 = a_3 \times 2 = 44 \times 2 = 88
\]
\[
a_5 = a_4 \times 2 = 88 \times 2 = 176
\]
\[
a_6 = a_5 \times 2 = 176 \times 2 = 352
\]
\[
a_7 = a_6 \times 2 = 352 \times 2 = 704
\]

Thus, the 7th term of the sequence is \( 704 \).

Therefore, the answer is:
\[
\boxed{704}
\]