In the formula, a 1 is the first term of the series, q is the common ratio of geometric series, and Sn is the sum of the first n terms. A sequence in which the ratio of each term to its previous term is equal to the same constant of the second term, usually expressed by G and P. This constant is called the common ratio of geometric series, usually expressed by the letter Q (q≠0), and the geometric series a 1≠ 0. Where each item in {an} is not 0. Note: When q= 1, an is a constant series.
The properties of the first n terms and formulas in proportional mathematics;
1, if m, n, p, q∈N+, and m+n=p+q, then am×an=ap×aq.
2. In the geometric series, every k term is added in turn, which is still a geometric series.
3. If G is the penultimate term in the equal proportion of A and B, G2=ab(G≠0).
4. If {an} is a geometric series, the common ratio is q 1, {bn} is also a geometric series, and the common ratio is q2, then {a2n}, {a3n,,, are geometric series, the common ratio is q12, and the common ratio is q13.
5. If (an) is a geometric series and all items are positive, and the common ratio is q, then (the logarithm of an based on log) is equal, and the tolerance is the logarithm of q based on log.
The first n terms of geometric series and formula skills
1, the sum formula of geometric progression's first n terms is Sn=n×a 1 (q= 1), and the sum formula of proportional series is the formula for geometric progression sum. If a series starts from the second term and the ratio of each term to the previous term is equal to the same constant, this series is called geometric series.
2. Geometric series refers to a series in which the ratio of each term to its previous term is equal to the same constant from the second term, usually expressed by G and P. This constant is called the common ratio of geometric series and usually expressed by the letter Q.