The nth term of a geometric sequence can be calculated using the formula:
Tn = a * r(n-1)
Where:
- Tn is the nth term of the sequence.
- a is the first term in the sequence.
- r is the common ratio between terms.
- n is the term number.
In our sequence, the first term a is 4.
To find the common ratio r, divide the second term by the first term (or any term by its previous term):
r = 8 / 4 = 2
Now that we have a = 4 and r = 2, we can write the formula for the nth term:
Tn = 4 * 2(n-1)
This formula allows us to find any term in the sequence. For example, if we want to find the 5th term:
T5 = 4 * 2(5-1) = 4 * 24 = 4 * 16 = 64
Thus, the 5th term of the sequence is 64. This formula applies to any term in this geometric sequence!