The given sequence is 3, 6, 12, 24. To find the 12th term, we first need to identify the pattern in the sequence.
Looking at the sequence, we can observe the following:
- The first term is 3.
- The second term (6) is obtained by multiplying the first term (3) by 2.
- The third term (12) is obtained by multiplying the second term (6) by 2.
- The fourth term (24) is obtained by multiplying the third term (12) by 2.
From this, we can see that each term in the sequence is generated by multiplying the previous term by 2:
General Formula: The formula for the nth term can be expressed as:
T(n) = 3 × 2^(n-1)
Now, if we want to find the 12th term (when n=12):
T(12) = 3 × 2^(12-1) = 3 × 2^11
Calculating this:
- 2^11 = 2048
- T(12) = 3 × 2048 = 6144
Thus, the 12th term of the sequence is 6144.