The sequence provided is 8, 16, 32, and 64. We can observe that this is a geometric progression where each term is multiplied by 2 to get the next term. To express this mathematically, we can identify the first term (a) and the common ratio (r).
The first term in this sequence, a, is 8. The common ratio, r, is calculated as follows:
- 16 / 8 = 2
- 32 / 16 = 2
- 64 / 32 = 2
Now, the formula for the nth term of a geometric sequence is given by:
T(n) = a * r^(n-1)
Here, T(n) is the nth term, a is the first term, r is the common ratio, and n is the term number you want to find.
In this case, we are looking for the thirteenth term (n = 13). Substituting the known values into the formula:
T(13) = 8 * 2^(13-1)
T(13) = 8 * 2^(12)
Now, we can calculate 2^12:
2^12 = 4096
Now, substituting this value back into the equation:
T(13) = 8 * 4096
T(13) = 32768
Therefore, the thirteenth term of the sequence 8, 16, 32, 64 is 32768.