Writing an explicit formula for geometric sequence

Site Navigation Geometric Sequences This lesson will work with arithmetic sequences, their recursive and explicit formulas and finding terms in a sequence. In this lesson, it is assumed that you know what an arithmetic sequence is and can find a common difference. If you need to review these topics, click here. This geometric sequence has a common ratio of 3, meaning that we multiply each term by 3 in order to get the next term in the sequence.

Writing an explicit formula for geometric sequence

Summary of the Process 1. Absent a stylesheet, a processor could not possibly know how to render the content of an XML document other than as an undifferentiated string of characters. This document is intended for implementors of such XSL processors.

Although it can be used as a reference manual for writers of XSL stylesheets, it is not tutorial in nature. While many of XSL's formatting objects and properties correspond to the common set of properties, this would not be sufficient by itself to accomplish all the goals of XSL. In particular, XSL introduces a model for pagination and layout that extends what is currently available and that can in turn be extended, in a straightforward way, to page structures beyond the simple page models described in this specification.

Because pagination introduces arbitrary boundaries pages or regions on pages on the content, concepts such as the control of spacing at page, region, and block boundaries become extremely important.

There are also concepts related to adjusting the spaces between lines to adjust the page vertically and between words and letters to justify the lines of text. These do not always arise with simple scrollable document windows, such as those found in today's browsers.

However, there is a correspondence between a page with multiple regions, such as a body, header, footer, and left and right sidebars, and a Web presentation using "frames". The distribution of content into the regions is basically the same in both cases, and XSL handles both cases in an analogous fashion.

XSL was developed to give designers control over the features needed when documents are paginated as well as to provide an equivalent "frame" based structure for browsing on the Web.

To achieve this control, XSL has extended the set of formatting objects and formatting properties. In addition, the selection of XML source components that can be styled elements, attributes, text nodes, comments, and processing instructions is based on XSLT and XPath [XPath]thus providing the user with an extremely powerful selection mechanism.

The actual extensions, however, do not always look like the DSSSL constructs on which they were based. There are several ways in which extensions were made.

writing an explicit formula for geometric sequence

In some cases, it sufficed to add new values, as in the case of those added to reflect a variety of writing-modes, such as top-to-bottom and bottom-to-top, rather than just left-to-right and right-to-left. In other cases, common properties that are expressed in CSS2 as one property with multiple simultaneous values, are split into several new properties to provide independent control over independent aspects of the property.

For example, the "white-space" property was split into four properties: The effect of splitting a property into two or more sub- properties is to make the equivalent existing CSS2 property a "shorthand" for the set of sub-properties it subsumes.

In still other cases, it was necessary to create new properties. For example, there are a number of new properties that control how hyphenation is done.

These include identifying the script and country the text is from as well as such properties as "hyphenation-character" which varies from script to script.

Some of the formatting objects and many of the properties in XSL come from the CSS2 specification, ensuring compatibility between the two. There are four classes of XSL properties that can be identified as: For example, the patterns of XPath allow the selection of a portion of a string or the Nth text node in a paragraph.

This allows users to have a rule that makes all third paragraphs in procedural steps appear in bold, for instance.

writing an explicit formula for geometric sequence

In addition, properties can be associated with a content portion based on the numeric value of that content portion or attributes on the containing element. This allows one to have a style rule that makes negative values appear in "red" and positive values appear in "black".

Also, text can be generated depending on a particular context in the source tree, or portions of the source tree may be presented multiple times with different styles. The layout structure is defined in terms of one or more instances of a "simple-page-master" formatting object.

This formatting object allows one to define independently filled regions for the body with multiple columnsa header, a footer, and sidebars on a page.

These simple-page-masters can be used in page sequences that specify in which order the various simple-page-masters shall be used. The page sequence also specifies how styled content is to fill those pages.

This model allows one to specify a sequence of simple-page-masters for a book chapter where the page instances are automatically generated by the formatter or an explicit sequence of pages such as used in a magazine layout. Styled content is assigned to the various regions on a page by associating the name of the region with names attached to styled content in the result tree.

In addition to these layout formatting objects and properties, there are properties designed to provide the level of control over formatting that is typical of paginated documents. This includes control over hyphenation, and expanding the control over text that is kept with other text in the same line, column, or on the same page.

This extended model is described in [4 Area Model] of this specification. The CSS2 box model is a subset of this model. The area model provides a vocabulary for describing the relationships and space-adjustment between letters, words, lines, and blocks.

Other directions are also used.Lena is asked to write an explicit formula for the graphed geometric sequence. The value, written as a decimal, should Lena use as the common ratio that is There exists the same question from other source with the image is shown/5(41). kcc1 Count to by ones and by tens.

kcc2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). kcc3 Write numbers from 0 to Represent a number of objects with a written numeral (with 0 representing a count of no objects).

kcc4a When counting objects, say the number names in the standard order, pairing each object with one and only. In this case, we can see that this is a geometric sequence with a geometric ratio equal to 20/-5 = / 20 or equal to 4.

Hence, r is equal to 4, a1 is equal to The geometric sequence formula is an = a1*r^(n-1) = -5 * (-4)^ (n-1) where n is an integer. Answer is B. Using Explicit Formulas for Geometric Sequences Because a geometric sequence is an exponential function whose domain is the set of positive integers, and the common ratio is the base of the function, we can write explicit formulas that .

Solve problems such as: The first four terms in a geometric sequence are 1/3, 1, 3, and 9. Find an explicit formula for the sequence. The explicit formula for a geometric sequence is of the form a n = a 1 r-1, where r is the common ratio.

A geometric sequence can be defined recursively by the formulas a 1 = c, a n+1 = ra n, where c is a constant and r is the common ratio.

Sequences and Series – She Loves Math