Derive the formula for calculation of geometric progression.

Answer 1

The formula for the general term (n-th term) of a geometric progression is given by:

an = a * r^(n-1),

where:
an = the n-th term,
a = the first term,
r = the common ratio, and
n = the position of the term in the sequence.

To derive this formula, we can start by considering the ratio between consecutive terms, which is denoted by r. Let's say we have the first term a, and the second term is ar. Since the second term is obtained by multiplying the first term by the common ratio r, we can express it as ar.

To find the third term, we multiply the second term by the common ratio r again, giving arr. Continuing this process, we can observe that the n-th term is obtained by multiplying the first term a by the common ratio r a total of (n-1) times.

So, by multiplying a by r^(n-1), we obtain the formula for the general term of a geometric progression:

an = a * r^(n-1).