SEQUENCEIn mathematics, asequenceis an ordered collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of thesequence.TERMInmathematical logic, atermdenotes a mathematical object and a formuladenotes a mathematical fact. In particular, terms appear as components of a formula.COMMON DIFFERENCEThe difference between each number in an arithmetic sequence.COMMON RATIOFor ageometric sequenceorgeometric series, the common ratio is theratioof atermto the previous term. This ratio is usually indicated by the variabler.ARITHMETIC MEANThe most commonly used type ofaverage. To find the arithmetic mean of asetofnnumbers, add the numbers in the set and divide the sum byn.ARITHMETIC SEQUENCEA sequence such as 1, 5, 9, 13, 17 or 12, 7, 2, 3, 8, 13, 18 which has a constant difference between terms. The first term is a1, the common difference is d, and the number of terms is n.GEOMETRIC MEANA kind of average. To find the geometric mean of a set of n numbers, multiply the numbers and then take the nth root of the product.GEOMETRIC SEQUENCEAsequencesuch as 2, 6, 18, 54, 162 orwhich has aconstantratiobetweenterms. The first term isa1, thecommon ratioisr, and the number of terms isn.INFINITE SEQUENCEAn infinite sequence is a list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integer s {1, 2, 3, ...}. Examples of infinite sequences are N = (0, 1, 2, 3, ...) and S = (1, 1/2, 1/4, 1/8, ..., 1/2 n , ...). The fact that a sequence is infinite is indicated by three dots following the last listed member.

FINITE SEQUENCEIn mathematics, a sequence is usually meant to be a progression of numbers with a clear starting point. Some sequences also stop at a certain number. In other words, they have a first term and a last term, and all the terms follow a specific order. This type of sequence is called a finite sequence. Let's go back to the rainbow example. Notice that the colors are listed as they appear in the rainbow, from the topmost down.Let's now look at a mathematical example. The first five positive odd numbers are an example of a finite sequence; it stops at the number 9: 1, 3, 5, 7, 9 The elements of a sequence are not an arbitrary list of numbers. In other words, they are not listed randomly, but follow a specific order. Often, finite sequences follow a specific mathematical pattern that can be represented by a general rule that can be displayed in algebraic terms or in words.FIBONACCI SEQUENCEThe sequence of numbers 1, 1, 2, 3, 5, 8, 13, 21, 34, . . . for which the next term is found by adding the previous two terms. This sequence is encountered in many settings, from population models to botany. Note: The sequence of ratios of consecutive terms has the Golden Mean as its limit.HARMONIC SEQUENCEIn mathematics, the harmonic series is the divergent infinite series: Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are 1/2, 1/3, 1/4, etc., of the string's fundamental wavelength.SERIESThe sum of the terms of a sequence. For example, the series for the sequence 1, 3, 5, 7, 9, . . . , 131, 133 is the sum 1 + 3 + 5 + 7 + 9 + . . . + 131 + 133.

10 Rules Of Subject Verb Agreement

Basic Rule.A singular subject (she, Bill, car) takes a singular verb (is, goes, shines), whereas a plural subject takes a plural verb.Example:Thelistof itemsis/are on the desk.If you know thatlistis the subject, then you will chooseisfor the verb.Rule 1.A subject will come before a phrase beginning withof. This is a key rule for understanding subjects. The wordofis the culprit in many, perhaps most, subject-verb mistakes.

Hasty writers, speakers, readers, and listeners might miss the all-too-common mistake in the following sentence:Incorrect:A bouquet of yellow roses lend color and fragrance to the room.Correct:Abouquetof yellow roseslends. . . (bouquet lends, notroses lend)Rule 2.Two singular subjects connected byor, either/or,orneither/norrequire a singular verb.Examples:Myauntor myuncleisarrivingby train today.NeitherJuannorCarmenisavailable.EitherKianaorCaseyishelpingtoday with stage decorations.Rule 3.The verb in anor, either/or,orneither/norsentence agrees with the noun or pronoun closest to it.Examples:Neither theplatesnor the servingbowlgoeson that shelf.Neither the servingbowlnor theplatesgoon that shelf.This rule can lead to bumps in the road. For example, ifIis one of two (or more) subjects, it could lead to this odd sentence:Awkward:Neither she, my friends, nor I am going to the festival.If possible, it's best to reword such grammatically correct but awkward sentences.Better:Neither she, I, nor my friends are going to the festival.ORShe, my friends, and I are not going to the festival.Rule 4.As a general rule, use a plural verb with two or more subjects when they are connected byand.Example:Acarand abikearemy means of transportation.But note these exceptions:Exceptions:Breaking and enteringisagainst the law.Thebed and breakfastwascharming.In those sentences,breaking and enteringandbed and breakfastare compound nouns.Rule 5.Sometimes the subject is separated from the verb by such words asalong with, as well as, besides, not,etc. These words and phrases are not part of the subject. Ignore them and use a singular verb when the subject is singular.Examples:Thepolitician, along with the newsmen,is expectedshortly.Excitement, as well as nervousness,isthe cause of her shaking.Rule 6.With words that indicate portionsa lot, a majority, some, all,etc.Rule 1 given earlier is reversed, and we are guided by the noun afterof. If the noun afterofis singular, use a singular verb. If it is plural, use a plural verb.Examples:A lotof thepiehas disappeared.A lotof thepieshave disappeared.Athirdof thecityisunemployed.Athirdof thepeopleareunemployed.Allof thepieisgone.Allof thepiesaregone.Someof thepieismissing.Someof thepiesaremissing.

Rule 7.In sentences beginning withhereorthere,the true subject follows the verb.Examples:Therearefourhurdlesto jump.Thereisa highhurdleto jump.Herearethekeys.

Rule 8.Use a singular verb with distances, periods of time, sums of money, etc., when considered as a unit.Examples:Three milesistoo far to walk.Five yearsisthe maximum sentence for that offense.Ten dollarsisa high price to pay.BUTTen dollars (i.e., dollar bills)werescattered on the floor.Rule 9.Some collective nouns, such asfamily, couple, staff, audience, etc., may take either a singular or a plural verb, depending on their use in the sentence.Examples:Thestaffis in a meeting.Staffis acting as a unit.Thecoupledisagreeabout disciplining their child.The couplerefers to two people who are acting as individuals.

Rule 10.The wordwerereplaceswasin sentences that express a wish or are contrary to fact:

Example:If Joewerehere, you'd be sorry.Shouldn'tJoebe followed bywas, notwere, given thatJoeis singular? But Joe isn't actually here, so we saywere, notwas. The sentence demonstrates thesubjunctive mood, which is used to express things that are hypothetical, wishful, imaginary, or factually contradictory. The subjunctive mood pairs singular subjects with what we usually think of as plural verbs.Examples:I wish itwereFriday.She requested that heraisehis hand.In the first example, a wishful statement, not a fact, is being expressed; therefore,were, which we usually think of as a plural verb, is used with the singular subjectI.

Normally,he raisewould sound terrible to us. However, in the second example, where a request is being expressed, the subjunctive mood is correct.

part of speechfunction or "job"example wordsexample sentences

Verbaction or state(to) be, have, do, like, work, sing, can, mustEnglishClubisa web site. IlikeEnglishClub.

Nounthing or personpen, dog, work, music, town, London, teacher, JohnThis is mydog. He lives in myhouse. We live inLondon.

Adjectivedescribes a nouna/an, the, 2, some, good, big, red, well, interestingI havetwodogs. My dogs arebig. I likebigdogs.

Adverbdescribes a verb, adjective or adverbquickly, silently, well, badly, very, reallyMy dog eatsquickly. When he isveryhungry, he eatsreallyquickly.

Pronounreplaces a nounI, you, he, she, someTara is Indian.Sheis beautiful.

Prepositionlinks a noun to another wordto, at, after, on, butWe wenttoschoolonMonday.

Conjunctionjoins clauses or sentences or wordsand, but, whenI like dogsandI like cats. I like catsanddogs. I like dogsbutI don't like cats.

Interjectionshort exclamation, sometimes inserted into a sentenceoh!, ouch!, hi!, wellOuch! That hurts!Hi! How are you?Well, I don't know.