The formula for finding the common ratio q is 1, the equal ratio median formula in geometric series,
Q = g/a = b/g If the former item A, the latter item B and the middle item G are known;
2. The general formula of geometric series,
An = a 1q (n- 1), called a 1, an and n,
Then q (n- 1) = an/a 1,
∴q=(an/a 1)^[ 1/(n- 1)。
What is geometric series, geometric series? The latter term is a series with the same proportion as the former term. This ratio is called the common ratio Q.
For example, 1248 16 ... The common ratio is 2.
Another example is 1/31/91/271/81... The common ratio is1/3.
Let the general term be an (item n), then a(n+ 1)=q*an.
Geometric series: a (n+ 1)/an = q, where n is a natural number.
(2) General formula: an = a1* q (n-1);
Generalization: an = am q (n-m);
(3) Sum formula: Sn=n*a 1(q= 1).
sn=a 1( 1-q^n)/( 1-q)
=(a 1-a 1q^n)/( 1-q)
= a1/(1-q)-a1/(1-q) * q n (that is, a-AQ n)
(Premise: Q is not equal to 1)
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