Find the 5th Term in the Sequence: 10, 20, 40, ...

To solve this problem, we need to determine the pattern in the sequence $10, 20, 40, \text{?,?,?}$.

The terms of the sequence seem to be generated by multiplying by a common ratio of 2. This is characteristic of a geometric sequence.

The first term $a_1 = 10$.

The second term is $a_2 = a_1 \times 2 = 10 \times 2 = 20$.

The third term is $a_3 = a_2 \times 2 = 20 \times 2 = 40$.

Following the pattern of multiplying by 2, we can determine the next terms:

• The fourth term $a_4 = a_3 \times 2 = 40 \times 2 = 80$.
• The fifth term $a_5 = a_4 \times 2 = 80 \times 2 = 160$.

Thus, the 5th element of the sequence is $160$.