Geometric progression's formula in senior high school is An = a 1q (n- 1), And geometric progression refers to a series in which the ratio of each item to its previous item is equal to the same constant starting from the second item, which is commonly expressed by G and P. An is a constant series.

The formula of proportional sequence is a formula for finding the sum of a certain number of geometric progression in mathematics. Geometric series are often used in life. In geometric series, when q≦- 1, or q=- 1 and k is odd, the sum of every k term in turn is still geometric series.

Common properties of geometric series {an};

(1) in the geometric series {an}, if m+n=p+q=2r(m, n, p, q, r∈N_), then am an = apaq = a.

Especially a1an = a2an-1= a3an-2 =.

(2) In the geometric series {an} with q, the sequences am, am+k, am+2k, am+3k, ... are still geometric series with q.

qk； Sequence Sm, S2m-Sm, S3m-S2m, ... or geometric series (at this time q ≦-1); an=amqn-m