9. the relationship between the general term an and the first n terms and Sn of a general sequence: an=
10, the general formula of arithmetic progression: an = a1+(n-1) d.
an=ak+(n-k)d
(where a 1 is the first term and ak is the known k term)
When d≠0, an is a linear equation about n; When d=0, an is constant.
1 1, arithmetic progression's first n terms and formula: Sn=
Serial number =
Serial number =
When d≠0, Sn is a quadratic form about n, and the constant term is 0; When d=0 (a 1≠0), Sn=na 1 is a proportional formula about n.
12, the general formula of geometric series:
Ann =
a 1
qn- 1
Ann =
Postal code of Alaska, USA
Quantum well
(where a 1 is the first term, ak is the known k term, and an≠0).
13, the first n terms of geometric series and formula: when q= 1, sn = n.
a 1
(it is a proportional formula about n);
When q≠ 1, Sn=
Serial number =
Third, the conclusion about arithmetic and geometric series.
Series Sm, S2m-Sm, S3m-S2m, S4m formed by the sum of any continuous m terms of 14 and arithmetic progression {an}.
-
S3m, ... It's still arithmetic progression.
15, arithmetic progression {an}, if m+n=p+q, then
16, geometric series {an}, if m+n=p+q, then
Series Sm, S2m-Sm, S3m-S2m, S4m formed by the sum of any continuous m terms of 17 and geometric series {an}.
-
S3m, ... is still a geometric series.
18, the sum and difference of two arithmetic progression {an} and {bn} series {an+bn} is still arithmetic progression.
19, a sequence consisting of the product, quotient and reciprocal of two geometric series {an} and {bn}
safe
bn}、。
、
Or geometric series.
20. arithmetic progression {an} Any equidistant series is still arithmetic progression.
2 1, the series of any equidistant term of geometric progression {an} is still geometric progression.
22. How to make three numbers equal: A-D, A, A+D; How to make four numbers equal: A-3D, A-D, A+D, A+3D?
23. How to make three numbers equal: A/Q, A, AQ;
Wrong methods of four numbers being equal: a/q3, a/q, aq, aq3.
(Why? )
24. If {an} is arithmetic progression, then
(c>0) is a geometric series.
25 、{ bn }(bn & gt； 0) is a geometric series, then {logcbn}
(c>0 and c
1)
It's arithmetic progression.
26.
In arithmetic progression.
Medium:
(1) If the number of items is
, then
(2) If the quantity is
Then,
27.
It grows geometrically.
Medium:
( 1)
If the number of items is
, then
(2) If the quantity is
Then,
Four, the common methods of sequence summation: formula method, split item elimination method, dislocation subtraction, reverse addition, etc. The key is to find the general item structure of the sequence.
28. Find the sum of series by grouping method: for example, an=2n+3n.
29. Sum by dislocation subtraction: for example, an=(2n- 1)2n.
30. Sum by split term method: for example, an= 1/n(n+ 1).
3 1, sum by addition in reverse order: for example, an=
32. The method of finding the maximum and minimum term of series {an}:
①
an+ 1-an=……
For example, a =
-2n2+29n-3
②
(An>0)
For example, a =
③
an=f(n)
Study the increase and decrease of function f(n)
For example, a =
33. In the arithmetic series
About Sn
-the maximum value problem solved by the commonly used adjacent term sign change method;
(1) When
& gt0, d<0, satisfied
The number of terms m makes
Take the maximum value.
(2) When
& lt0, d>0, satisfied
The number of terms m makes
Take the minimum value.
We should pay attention to the application of the transformation idea when solving the maximum problem of the sequence with absolute value.