* Find the common ratio for a geometric sequence.
* List the terms of a geometric sequence.
* Use a recursive formula for a geometric sequence.
* Use an explicit formula for a geometric sequence.
Find the nth term of a sequence
Find the index of a given term of a sequence
Given a geometric series, be able to calculate the nth partial sum
Identify a geometric series as convergent or divergent.
* Find the common difference for an arithmetic sequence.
* Write terms of an arithmetic sequence.
* Use a recursive formula for an arithmetic sequence.
* Use an explicit formula for an arithmetic sequence.
Find the nth term of a sequence
Find the index of a given term of a sequence
Given a geometric series, be able to calculate the nth partial sum
Identify a geometric series as convergent or divergent.
* Find the common difference for an arithmetic sequence.
* Write terms of an arithmetic sequence.
* Use a recursive formula for an arithmetic sequence.
* Use an explicit formula for an arithmetic sequence.
* Use summation notation.
* Use the formula for the sum of the first n terms of an arithmetic series.
* Use the formula for the sum of the first n terms of a geometric series.
* Use the formula for the sum of an infinite geometric series.
* Solve annuity problems.
* Evaluate square roots.
* Use the product rule to simplify square roots.
* Use the quotient rule to simplify square roots.
* Add and subtract square roots.
* Rationalize denominators.
* Use rational roots.
* Model exponential growth and decay
* Use Newton's Law of Cooling
* Use logistic-growth models
* Choose an appropriate model for data
* Express an exponential model in base e
* Construct perpendicular and angle bisectors
* Use bisectors to solve problems
* Identify the circumcenter and incenter of a triangle
* Use triangle segments to solve problems
* Use summation notation.
* Use the formula for the sum of the first n terms of an arithmetic series.
* Use the formula for the sum of the first n terms of a geometric series.
* Use the formula for the sum of an infinite geometric series.
* Solve annuity problems.
* Evaluate square roots.
* Use the product rule to simplify square roots.
* Use the quotient rule to simplify square roots.
* Add and subtract square roots.
* Rationalize denominators.
* Use rational roots.
* Model exponential growth and decay
* Use Newton's Law of Cooling
* Use logistic-growth models
* Choose an appropriate model for data
* Express an exponential model in base e
* Construct perpendicular and angle bisectors
* Use bisectors to solve problems
* Identify the circumcenter and incenter of a triangle
* Use triangle segments to solve problems
* Identify, write, and analyze conditional statements
* Write the inverse, converse, and contrapositive of a conditional statement
* Write a counterexample to a fake conjecture
* Find the distance between two points
* Find the midpoint of two given points
* Find the coordinates of an endpoint given one endpoint and a midpoint
* Find the coordinates of a point a fractional distance from one end of a segment
* Connect functions to their graphs
* Graph piecewise-defined functions
* Graph absolute value functions
* Graph greatest-integer functions
* Interpret graphs
* Use the vertical line test to determine a function
* Connect functions to their graphs
* Graph piecewise-defined functions
* Graph absolute value functions
* Graph greatest-integer functions
* Interpret graphs
* Use the vertical line test to determine a function
* Introduce functions and function notation
* Develop skills in constructing and interpreting the graphs of functions
* Learn to apply this knowledge in a variety of situations
* Recognize graphs of common functions.
* Graph functions using vertical and horizontal shifts.
* Graph functions using reflections about the x-axis and the y-axis.
* Graph functions using compressions and stretches.
* Combine transformations.
* Identify intervals on which a function increases, decreases, or is constant
* Use graphs to locate relative maxima or minima
* Test for symmetry
* Identify even or odd functions and recognize their symmetries
* Understand and use piecewise functions
* Solve polynomial equations by factoring
* Solve equations with radicals and check the solutions
* Solve equations with rational exponents
* Solve equations that are quadratic in form
* Solve absolute value equations
* Determine whether a relation or an equation represents a function.
* Evaluate a function.
* Use the vertical line test to identify functions.
* Identify the domain and range of a function from its graph
* Identify intercepts from a function’s graph
* Solve counting problems using the Addition Principle.
* Solve counting problems using the Multiplication Principle.
* Solve counting problems using permutations involving n distinct objects.
* Solve counting problems using combinations.
* Find the number of subsets of a given set.
* Solve counting problems using permutations involving n non-distinct objects.
* Write the terms of a sequence defined by an explicit formula.
* Write the terms of a sequence defined by a recursive formula.
* Use factorial notation.
* Identify characteristics of each type of conic section
* Identify a conic section from its equation in general form
* Identifying the eccentricities of each type of conic section
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
2. Concepts and Objectives
⚫ The objectives for this section are
⚫ Find the common ratio for a geometric sequence.
⚫ List the terms of a geometric sequence.
⚫ Use a recursive formula for a geometric sequence.
⚫ Use an explicit formula for a geometric sequence.
3. Geometric Sequences
⚫ A geometric sequence is a sequence in which each term
equals a constant multiplied by the preceding term.
⚫ The constant for a geometric sequence is called the
common ratio, r, because the ratio between any two
adjacent terms equals this constant.
⚫ Like arithmetic sequences, formulas for calculating an for
geometric sequences can be found by linking the term
number to the term value.
5. Geometric Sequences (cont.)
⚫ Consider the geometric sequence:
3, 6, 12, 24, 48, …
This sequence has a1 = 3 and common ratio r = 2. Thus:
=
1 3
a
=
2 3 2
a
= = 2
3 3 2 2 3 2
a
= = 3
4 3 2 2 2 3 2
a
−
= 1
3 2n
n
a
6. Geometric Sequences (cont.)
⚫ The nth term of a geometric sequence equals the first
term multiplied by (n – 1) common ratios. That is,
⚫ A geometric sequence is actually just an example of an
exponential function. The only difference is that the
domain of a geometric sequence is rather than all real
numbers.
−
= 1
1
n
n
a a r
8. Examples
1. Calculate a100 for the geometric sequence with first
term a1 = 35 and common ratio r = 1.05.
( )( )
−
= 100 1
100 35 1.05
a
( )( )
99
35 1.05 4383.375262
= =
9. Examples
2. Write an explicit formula for the nth term of the
following geometric sequence:
{2, 10, 50, 250, …}
10. Examples
2. Write an explicit formula for the nth term of the
following geometric sequence:
{2, 10, 50, 250, …}
The first term, a1, is 2. The common ratio can be found
by dividing the second term by the first term:
10
5
2
r = =
11. Examples
2. Write an explicit formula for the nth term of the
following geometric sequence:
{2, 10, 50, 250, …}
The nth term can be found by plugging these values into
the formula:
( )
1
2 5n
n
a −
=
