The formula for the nth term of a geometric sequence is an = a1(r)^(n-1).
- an represents the nth term of the sequence.
- a1 represents the first term of the sequence.
- r represents the common ratio, the constant factor that multiplies each term to get the next.
- n represents the position of the term in the sequence.
For example, consider the geometric sequence 2, 4, 8, 16...
- a1 = 2 (the first term)
- r = 2 (the common ratio, as each term is twice the previous one)
To find the 5th term (a5), we plug the values into the formula:
- a5 = 2(2)^(5-1) = 2(2)^4 = 2(16) = 32
Therefore, the 5th term of this geometric sequence is 32.
This formula is essential for understanding and working with geometric sequences. It allows you to find any term in the sequence, given the first term and the common ratio.
