The general nth term of the sequence 3, 6, 12, 24 can be derived by observing the pattern in the sequence. Notice how each term is formed:
- The first term is 3.
- The second term is 6, which is 3 multiplied by 2.
- The third term is 12, which is 6 multiplied by 2.
- The fourth term is 24, which is 12 multiplied by 2.
It appears that each term is double the previous term. This is a geometric sequence where the first term a is 3 and the common ratio r is 2.
The formula for the nth term T(n) of a geometric sequence can be expressed as:
T(n) = a * r^(n-1)
Substituting the known values into the formula:
T(n) = 3 * 2^(n-1)
So, the general nth term of the sequence 3, 6, 12, 24 is:
T(n) = 3 * 2^(n-1)