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!

- 10th arithmetic progression solves ... by Akshay Fegade 98906 views
- Arithmetic progression by Mayank Devnani 24235 views
- Class 10 arithmetic_progression_cbs... by dinesh reddy 119 views
- 5.2 arithmetic sequences by math123c 1423 views
- Arithmetic progressions - Problems ... by Let's Tute 543 views
- Probability - Question Bank for Cla... by Let's Tute 6278 views

No Downloads

Total views

2,132

On SlideShare

0

From Embeds

0

Number of Embeds

454

Shares

0

Downloads

78

Comments

0

Likes

2

No embeds

No notes for slide

- 1. Arithmetic Progression T- 1-855-694-8886 Email- info@iTutor.com By iTutor.com
- 2. Arithmetic Progression a) 5, 8, 11, 14, 17, 20, … 3n+2, … b) -4, 1, 6, 11, 16, … 5n – 9, . . . c) 11, 7, 3, -1, -5, … -4n + 15, . . . In all the lists above, we see that successive terms are obtained by adding a fixed number to the preceding terms. Such list of numbers is said to form an Arithmetic Progression ( AP ). So,an arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number to the 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 © iTutor. 2000-2013. All Rights Reserved
- 3. nth term of arithmetic sequence Tn = a + d(n – 1) a = First term d = common difference n = number of terms. Common difference = the difference between two consecutive terms in a sequence. d = Tn – Tn-1 Example Find the nth term of the following AP. © iTutor. 2000-2013. All Rights Reserved
- 4. Finding the 956th term 56, 140, 124, 108, . . . Tn = a + d(n – 1) T956 = 156 + -16(956 – 1) T956 = 156 - 16(955) T956 = 156 - 15280 T956 = -15124 a1 = 156 d = -16 n = 956 Example Finding the number of terms in the AP 10, 8, 6, 4, 2, . . .-24 Tn = a + d(n – 1) -24 = 10 -2(n – 1) -34 = -2(n – 1) 17 = n-1 n = 18 a = 10 d = -2 Tn = -24 © iTutor. 2000-2013. All Rights Reserved
- 5. The 5th term of an AP is 13 and the 13th term is -19. Find the first term & the common difference. T5 = a + 4d = 13……..(1) T13= a + 12d = -19……….(2) (2) – (1): 8d = -19 - 13 8d = - 32 d = -4 Substitute d = -4 into (1): a + 4(-4) = 13 a – 16 = 13 a = 29© iTutor. 2000-2013. All Rights Reserved
- 6. Sn = a1 + (a1 + d) + (a1 + 2d) + …+ an Sn = an + (an - d) + (an - 2d) + …+ a1 2 )( 1 1 n n i in aan aS + == ∑= )(2 1 nn aanS += )(...)()()(2 1111 nnnnn aaaaaaaaS ++++++++= Sum of First terms of an AP © iTutor. 2000-2013. All Rights Reserved
- 7. 1 + 4 + 7 + 10 + 13 + 16 + 19 a1 = 1 an = 19 n = 7 2 )( 1 n n aan S + = 2 )191(7 + =nS 2 )20(7 =nS 70=nS Example Find the sum of the integers from 1 to 100 a1 = 1 an = 100 n = 100 2 )( 1 n n aan S + = 2 )1001(100 + =nS 2 )101(100 =nS 5050=nS © iTutor. 2000-2013. All Rights Reserved
- 8. Find the sum of the multiples of 3 between 9 and 1344 a1 = 9 an = 1344 d = 3 2 )( 1 n n aan S + = 2 )13449( + = n Sn 2 )1353(446 =nS 301719=nS )1(1 −+= ndaan )1(391344 −+= n 3391344 −+= n 631344 += n n31338 = n=446 Sn = 9 + 12 + 15 + . . . + 1344 © iTutor. 2000-2013. All Rights Reserved
- 9. Find the sum of the multiples of 7 between 25 and 989 a1 = 28 an = 987 d = 7 2 )( 1 n n aan S + = 2 )98728( + = n Sn 2 )1015(138 =nS 70035=nS )1(1 −+= ndaan )1(728987 −+= n 7728987 −+= n 217987 += n n7966 = n=138 Sn = 28 + 35 + 42 + . . . + 987 © iTutor. 2000-2013. All Rights Reserved
- 10. Evaluate a1 = 16 an = 82 d = 3 n = 23 2 )( 1 n n aan S + = 2 )8216(23 + =nS 2 )98(23 =nS 1127=nS Sn = 16 + 19 + 22 + . . . + 82 ∑= + 25 3 )73( i i © iTutor. 2000-2013. All Rights Reserved
- 11. Review -- Arithmetic nth term Sum of n terms )1(1 −+= ndaan 2 )( 1 n n aan S + = © iTutor. 2000-2013. All Rights Reserved
- 12. The End Call us for more information: www.iTutor.com 1-855-694-8886 Visit

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