Arithmetic progression (a.p.), Mathematics

Assignment Help:

A series is said to be in Arithmetic Progression (A.P.) if the consecutive numbers in the series differs by a constant value. This constant value is referred to as "common difference". The series in which the consecutive terms increases by a constant quantity, is referred to as an increasing series and if the terms decrease by a constant quantity it is referred to as a decreasing series. The series

                            3, 7, 11, 15, 19, .............

is an example of increasing series, while the one like

                            8, 2, -4, .........

is an example of decreasing series.

In an A.P. the first number is denoted by "a" and the common difference is denoted by "d". If we know the values of a and d, it is quite easy to get the terms of the Arithmetic Progression. In terms of a and d, the consecutive terms of arithmetic progression are

                   a, a + d, a + 2d, a + 3d, ......... a + nd

We observe that the first term is a, the second term is a + d, the third term being a + 2d. The point to note is that for the first term the coefficient of d is zero, for the second term it is one and for the third term it is 2. By observing this pattern can we conclude that the coefficient of nth term is n - 1? Yes, we can. In fact, the nth term is given by

                    Tn  = a + (n - 1)d

Generally the Tn  which is the last term is also denoted by "l" (small alphabet 'l'). That is, l = a + (n - 1)d.

Now let us look at an example.

Example 

If the first term of an A.P. 'a' = 3 and the common difference 'd' = 2, what are the first five terms of the series and what would be the nth term? They are calculated as follows. We know that

                   T1     = a                = 3

                   T2     = a + d           = 3 + 2 = 5

                   T3     = a + 2d         = 3 + 2(2) = 7

                   T4     = a + 3d         = 3 + 3(2) = 9

                   T5     = a + 4d         = 3 + 4(2) = 11

                   :                                          :
                   :                                          :

           l = Tn        = a + (n - 1)d  = 3 + (n - 1)(2)

                                                = 3 + 2n - 2

                                                = 2n + 1


Related Discussions:- Arithmetic progression (a.p.)

What is the connecticut sales tax on this item, Connecticut state sales tax...

Connecticut state sales tax is 6%. Lucy purchases a picture frame in which costs $10.50 What is the Connecticut sales tax on this item? Find out 6% of $10.50 by multiplying $10

Decision-making under conditions of certainty, Decision-Making Under Condit...

Decision-Making Under Conditions of Certainty Conditions of certainty tend to be rare, especially when significant decisions are involved. Under conditions of certainty, decis

Positive skewness-measure of central tendency, Positive Skewness - It ...

Positive Skewness - It is the tendency of a described frequency curve leaning towards the left. In a positively skewed distribution, the long tail extended to the right. In

Help, can you help me with math

can you help me with math

Bussiness, How do these websites help the company strengthen its relationsh...

How do these websites help the company strengthen its relationships with its stakeholders? List the website(s) that you previewed and give examples to support your answers. Who are

Find out the roots of the quadratic equation, Find out the roots of the fol...

Find out the roots of the following quadratic equation. 3x 2 + 7x = 0 Solution: Using Equation 6, one root is determined. x = 0 Using Equation 7, substitute the

Find out a if f(x) is continuous at x = -2 , Example   Given the graph of ...

Example   Given the graph of f(x), illustrated below, find out if f(x) is continuous at x = -2 , x = 0 , and x = 3 . Solution To give answer of the question for each

Example of line - common polar coordinate graphs, Example of line - Common ...

Example of line - Common Polar Coordinate Graphs Example:  Graph θ = 3Π, r cos θ = 4 and r sin θ = -3 on similar axis system. Solution There actually isn't too much to

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd