Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

- Arithmetic progression by Mayank Devnani 17543 views
- 10th arithmetic progression solves ... by Akshay Fegade 86532 views
- Arithmetic progression by Rajaram Narasimhan 15198 views
- Arithmatic progression by Aditya Kumar Pathak 16532 views
- Maths project work - Arithmetic Seq... by S.L.B.S Engineeri... 10313 views
- Arithmetic progression by Chhavi Bansal 8044 views

20,554 views

19,827 views

19,827 views

Published on

No Downloads

Total views

20,554

On SlideShare

0

From Embeds

0

Number of Embeds

10

Shares

0

Downloads

981

Comments

0

Likes

11

No embeds

No notes for slide

- 1. You must have observed that in nature, many things follow a certain pattern, such as the petals of sun flower, the holes of a honeybee comb, the grains on a maize cob, the spirals on a pineapple and on a pine cone etc. We now look for some patterns which occur in our daily life. For example: Mohit applied for a job and got selected. He has been offered a job with a starting monthly salary Rs 8000, with an annual increment of Rs 500 in his salary. His salary for the 1st, 2nd,3rd,…years will be, respectively 8000, 8500, 9000,…..
- 2. In the above example, we observe a pattern. We find that the succeeding terms are obtained by adding a fixed number(500).
- 3. Consider the following lists of numbers: 1) 1,2,3,4….. 2) 100,70,40,10… 3) -3,-2,-1, 0…. 4) 3, 3, 3, 3……. 5) -1.0, -1.5, -2.0, -2.5,……. Each of the numbers in the list is called a term.
- 4. Given a term, can you write the next term in each of the lists above? If so, how will you write it? Perhaps by following a pattern or rule. Let us observe and write the rule: In(1), each term is 1 more than the term preceding it. In(2), each term is 30 less than the term preceding it. In(3), each term is obtained by adding 1 to each term preceding it. In(4), all the terms in the list are 3, ie, each term is obtained by adding 0 to the term preceding it. In(5), each term is obtained by adding - 0.5 to the term preceding it.
- 5. In all the lists above, we see that the successive terms are obtained by adding a fixed number to the preceding terms. Such lists are called ARITHMETIC PROGRESSIONS (or) AP. So, An Arithmetic Progression is a list of numbers in which each term is obtained by adding a fixed number preceding term except the first term. This fixed number is called the common difference of the AP. Remember that it can be positive(+), negative(-) or zero(0)
- 6. Let us denote the first term of an Arithmetic Progression by (a1)second term by (a2 ), nth term by (ax ) and the common difference by d . The general form of an Arithmetic Progression is : a , a +d , a + 2d , a + 3d ………………, a + (n-1)d Now, let us consider the situation again in which Mohit applied for a job and been selected. He has been offered a starting monthly salary of Rs8000, with an annual increment of Rs500. what would be his salary for the fifth year?
- 7. The nth term an of the Arithmetic Progression with first term a and common difference d is given by an=a+(n-1) d. an is also called the general term of the AP. If there are m terms in the Arithmetic Progression , then am represents the last term which is sometimes also denoted by l. The sum of the first n terms of an Arithmetic Progression is given by s=n/2[2a+(n-1) d]. We can also write it as s=n/2[a +a+(n-1) d].
- 8. •The first term = a1 =a +0 d = a + (1-1)d Let us consider an A.P. with first term ‘a’ and common difference ‘d’ ,then •The second term = a2 = a + d = a + (2-1)d •The third term = a3 = a + 2d = a + (3-1)d •The fourth term = a4 =a + 3d = a + (4-1)d The nth term = an = a + (n-1)d
- 9. To check that a given term is in A.P. or not. 2, 6, 10, 14…. (i) Here , first term a = 2, find differences in the next terms a2-a1 = 6 – 2 = 4 a3-a2 = 10 –6 = 4 a4-a3 = 14 – 10 = 4 Since the differences are common. Hence the given terms are in A.P.
- 10. Now let’s try a simple problem: Problem :Find 10th term of A.P. 12, 18, 24, 30…… Solution: Given A.P. is 12, 18, 24, 30.. First term is a = 12 Common difference is d = 18- 12 = 6 nth term is an = a + (n-1)d Put n = 10, a10 = 12 + (10-1)6 = 12 + 9 x 6 = 12 + 54 a10 = 66
- 11. Problem 2. Find the sum of 30 terms of given A.P. 12 + 20 + 28 + 36……… Solution : Given A.P. is 12 , 20, 28 , 36 Its first term is a = 12 Common difference is d = 20 – 12 = 8 The sum to n terms of an arithmetic progression Sn = ½ n [ 2a + (n - 1)d ] = ½ x 30 [ 2x 12 + (30-1)x 8] = 15 [ 24 + 29 x8] = 15[24 + 232] = 15 x 246 = 3690

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment