How many ways to find an?? Five ways to find An

Five ways to find an:

Formula method. s1（n=1），an=s-s（n≥2）nn-1-。

Superposition: If an+1=an+f(n), then: an=a1+k=2(ak-ak-1)=a1+k=2f(k-1)=a1+k=1f(k) nnn-1-.

Stacking and multiplication method: If an+1=f(n)an, then: a2a3anan=a1aa....a=a1f（1）f（2）…f（n-1）（n≥2）n-112。

Factorization: By appropriate identity deformation, such as formulation, factorization.

Take the logarithm. Through appropriate answers, the identity of the deformation such as formula, factorization, logarithm, reciprocal, etc., into the equal ratio of the oak number series or the equal difference series.

Meaning:

Formulas containing equal signs are called equations. Equations can be divided into contradictory equations and conditional equations. Add (or subtract) the same integer to both sides of the equation at the same time.

Either both sides of the equation are multiplied or divided by the same non-0 integer, or both sides of the equation are multiplied at the same time, and the equation still holds. The form is to connect two equal numbers (or numbers represented by letters) with "=".

Use an: When the modified name starts with a vowel (pay special attention: it is pronounced as a vowel and not a letter is a vowel letter), use an, e.g. an interesting book

Use a: and a is used for words that start with a consonant, e.g. a happy ending When the first pronunciation of a noun is a vowel phonetic transcription, use an eg: an eye, an ear

When the first pronunciation of a noun is a consonant phonetic transcription, use a eg:a hand

The determination of the indefinite article a,an in front of the English letter u gives students a headache.

How to master it? It's simple, you send the alphabet.

The word that is pronounced by an a, and the word that does not pronounce the alphabet is preceded by an:a university.

a useful book an umbrella.

An Underground Train is a subway train.

1. Equation for equal difference series.

The formula for the difference series is an=a1+(n-1)d

The sum of the first n terms is: sn=na1+n(n-1)d 2 if the tolerance d=1: sn=(a1+an)n 2 if m+n=p+q: am+an=ap+aq, if m+n=2p, then: am+an=2ap

The above n are positive integers.

Text translation. The value of the nth term an = first term + (number of terms - 1) tolerance.

The sum of the n terms of the previous calendar is sn=the first term + the last term The number of terms (number of terms-1) tolerance 2 tolerance d=(an-a1) (n-1).

Number of Items = (Last Item - First Term) Tolerance + 1

2. The formula for summing terms in the equal difference series.

When the number column is an odd number, the sum of the first n terms = the number of middle terms.

The number column is an even number, add the first and last terms, and divide its sum by the middle of the difference of 2. The formula 2an+1=an+an+2 is a series of equal differences.

A1 is the first term, An is the general formula of the nth term, and D is the tolerance.

The formula for the sum of the first n terms is: sn=na1+n(n-1)d 2sn=(a1+an)n 2

If m+n=p+q, then: am+an=ap+aq, if m+n=2p, then: am+an=2ap

All of the above are positive integers.

The value of the nth term an = first term + (number of terms - 1) tolerance.

The sum of the first n terms sn=first term n + number of terms (number of terms-1) tolerance 2 tolerance d=(an-a1) (n-1).

Number of Items = (Last Item - First Term) Tolerance + 1

When the number column is an odd number, the sum of the first n terms = the number of intermediate terms.

The number column is an even number of terms, find the first and last terms, divide it by 2 equal differences, and divide the middle term formula 2an+1=an+an+2, where is the equal difference series.

General term formulas. Tolerance Number of items + first term - tolerance.

Accumulation. Example 3

It is known that a1=1, an+1=an+2n

Finding the AN solution: From the recursive formula: a2-a1=2, a3-a2=22, a4-a3=23, an-an-1=2n-1

Add the above n-1 equations to get it.

an=a1+2+22+23+24+…+2n-1=1+2+22+23+…+2n-1=2n-1

Note: Difference accumulation can be used for series with recursive formulas such as an+1=an+f(n).

In particular, when f(n) is a constant, the series is a series of equal differences.

Stack multiplication. Example 4

It is known that a1=1, an=2nan-1(n 2) to find an solution: when n 2, 22, 23, 24 ,...

2nMultiply the above n-1 formulas to get the royal fight.

an=bury + n=2

When n=1, a1=1 satisfies the above equation.

Therefore an=2n n*).

Note: For the series of recursive formulas such as an+1an=g(n), the general term formula can be found by quotient stacking and multiplication, in particular, when the town is liquid auspicious g

n) is a constant, and the sequence is proportional.

A is used to pronounce a letter or word that begins with a consonant phoneme. For example: apen a pen, abook a book; An is pronounced before a letter or word that begins with a vowel phoneme.

For example: anapple an apple, anorange an orange, anegg an egg, anenglishbook an englishbook extension material special usage: 1. Although the first letter of some words begins with a vowel letter, when its pronunciation begins with a consonant sound Li Qingdousu, the article in front of it cannot use an like a word that begins with a general vowel letter, but should use the article a.

For example: ausefulbook is a useful book. Book 2, although the word "useful" begins with the vowel letter u, but its pronunciation is [jusfl] that begins with the consonant factor, so it can not be preceded by the article an, but should be preceded by the article Although the first letter of some words is a consonant letter, when its pronunciation begins with a vowel phoneme, the article before it can not be used a, but should be used an.

For example: anhour for an hour. 4. Although the word "hour" begins with the consonant letter h, it is pronounced with vowel sounds.

Calendar segments. 1. Add an before words that begin with vowel letters a, e, i, o. Some words that start with u do not need to be preceded by an.

Such as UFO, useful, university, etc., some use plus AN. Such as umbrella, uncle, etc.

Words that begin with vowel letters, but whose pronunciation begins with consonants, are as follows

The spelling of words such as ufo, useful, university, usual, united, european, one-eyed, one-way, etc., although they start with vowel letters, their pronunciation begins with consonants, so they should be preceded by a. Except for umbrella, uncle, etc., because the pronunciation starts with a vowel, therefore, an should be used in front.

Second, summarize the law as rotten:

Among the 26 English letters, the pronunciation of 12 letters, A, E, I, O, F, H, L, M, N, R, S, and x begins with vowels. Start with these 12 letters and add an before the word. For example, Apple, Eraser, Hour, etc.

Words that start with 14 letters other than a, e, i, o, f, h, l, m, n, r, s, x are preceded by a. For example, book, car, door, etc.

A and an are used smoothly: the indefinite articles a and an, before the singular countable noun; If the consonant is first written in the word, only a is added before the word; If the vowel is played at the beginning of the word, the word before the word dare not be forgotten; The indefinite article is quite one, but does not emphasize the concept of numbers; The indefinite article is crucial, and the four referents are remembered. (Each refers to a precursor circle, a generic signifier, a generic signifier and a certain sign).

"a" and "an" are indefinite articles, and for pronunciation convenience, an is used instead of a before the singular noun of a countable noun that begins with a vowel phoneme.

Usage of a and an:

Used in front of words that begin with a consonant letter, or that begins with a vowel letter pronounced as a consonant.

Used in front of words that begin with a vowel letter (a, e, i, o, u) or an unpronounced h.

It is also used in front of a single letter that begins with a yuan.

There are no sexual changes.

And an is used to guess the first noun mentioned in the singular form of a countable noun, which is used to refer to a noun mentioned for the first time in our conversation.

And an is used before a singular noun, of course, it is still a countable noun, indicating - human-like or thing, which is more special and refers to it in general.

7. A and An can be used in **, speed, ratio ratio, frequency and so on. A and an are equivalent to "each" and "one".

8. A and an can be used in some fixed phrases, mainly related to quantity.

This is an obvious interleaved sequence, n is odd when an=1, n is even, an=-1 (n=1, 2, 3...).Therefore an=(-1) (nm), where m is any odd number.

Recursive formula: If the relationship between the nth term of a series and its previous terms can be expressed by a formula, then this formula is called the recursive formula of the series. Features of the recursive formula of the number series:

1) The recursive formula for some series of tremors can have different forms, i.e., they are not unique.

2) Some sequences do not have recursive formulas, that is, there are recursive formulas and there are not necessarily general formulas.

There are infinite sequences and infinite sequences:

The number of terms is arbitrarily assigned to a finite sequence of numbers; A column with an infinite number of items is an infinite sequence.

For positive sequences: (If all items of the series are positive, it is a positive sequence).

1) From the second term onwards, the number series in which each term splits its finger is greater than its previous term is called an increasing series; Such as: 1, 2, 3, 4, 5, 6, 7.

2) From the 2nd term onwards, the sequence in which each term is smaller than its predecessor is called a decreasing sequence; Such as: 8, 7, 6, 5, 4, 3, 2, 1.

3) From the 2nd term onwards, a series of numbers in which some terms are greater than its predecessor and some terms are smaller than its predecessor is called a swinging sequence (swinging sequence).

3) Periodic sequence: A sequence in which each item changes periodically is called a periodic sequence (such as a trigonometric function).

4) Constant sequence: A sequence of equal terms is called a constant sequence (e.g., 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2).