Name Date: Worksheet 8.2 + 8+ 8 + 8 an = a, + d ( h -1 ) 1. Put in summation notation: 2 + 10 + 18 + 26+ 34+ 42 + 50 50 = 2+18 (1 - 1 ) 5 8n - 6 50 =2 + 8 h -8 1 = 1 n = ? 56 - 81 50 =46 + 8 h 2. Put in summation notation: 120 + 116 + 112 + 108 + ... + 32 8 8 +6 +6 2 3 = = 4 an = 126 + - 4 (1 - 1) ( Un+ 124 ) 120 - 4,+4 32 - 124 - in 3 . Find the sum of: 15 (3n - 2) 4. Find the sum of the first 20 terms of: 3 + 8 + 13 + 18 + ... 5. The first row in a theater has 36 seats and each successive row has 2 additional seats. If there are 114 seats in the last row, how many rows are there and how many seats are there in the theater? 6. Solve for x : 15 ( 2n + x ) = 285 n=1 7. The first three terms of an arithmetic sequence are x, 3x + 4, and 18. Determine the sum of the first ten terms of this sequence.8. An iron ball will fall 16.1 ft the first second, 48.3 ft the next second, 80.5 ft the third second, etc. At the end of 30 seconds, what is the total distance it has fallen? 9. If you saved 10 cents during the first week of January, 20 cents during the second week, 30 cents during the third week and so on, how much will you have saved in all at the end of 52 weeks. Answers: (8n - 6) 10. Find the sum: (hint: you can't just plug 0 into the equation!) (-4n +124) ( 2 n + 1 ) 3. 330 4 . 1010 5. 40 rows, 3000 seats 6. 3 7. 380 8 . 14,490 ft 11. Find the sum of the series denoted by : 9 . $137.80 20 10. 2704 ( 5n + 3 ) 11. 1110 n=1 32 ( 3n + 2 ) n=1 15. 4578 16. 56 17. 4, 6, 8, 10 12. Write in summation notation: 5 + 8 + 11 + 14 + ... + 98. 18. 2 19. 576 ft 20. 120 logs 21. $14.50; $379.75 22. 2816 23. 49 13. Find the sum of the series denoted by: (hint: you can't just plug 4 and 45 into the equation!) (4x + 11) x=4 14. How many multiples of 8 are between 53 and 501? 15. Find the first 4 terms of an arithmetic series whose sum is defined by: Sn = n + 3n16. Find the value of a: (an + 7 ) = 65 17. You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second and so on in an arithmetic sequence. What is the total distance the object will fall in 6 seconds? 18. There is a stack of logs in the backyard. There are 15 logs in the first layer, 14 in the second, 13 in the third and so on with the last layer having 1 log. How many logs are in the stack? 19. In his piggy bank, Bingo dropped $1.00 on May 1st, $1.75 on May 2nd, $2.50 on May 3"d and so on until the last day of May. How much did he drop in his piggy bank on May 19th? How much did he put in his piggy bank in the month of May? 20. A theater has 32 rows of seats. If there are 26 seats in the 1st row, 30 in the 2nd, 34 in the third, and so on, how many seats are there in all? 21. How many terms are in the sequence: 19, 26, 33, ... 355?1 a (when added 1+3 + 5 + 7 + 9 Ft/ - 36 + 6 = 6 add them up + dride 4 = 6 by # of It's (11+ 1 ) ( 6 ) , then mult by # OF H'S - SUM Ist term + last term then minde love ? alan 3 6 >last # & + an - 7 formula to find the 2. sum same as ~ an = 4 4- 12 find the sum or the first 100 FF 'S 4 - 12 d , = - 8 100 (- 8 + 3 8 8 ) 400 2 - 12 196 - 14000 a = 4 ( 1 ) - 12 = - 8 9 100 = 4 ( 10 0 ) - 12 - 38 8 389 +8 2 380 sand 100 Problem h = 160 140+100 = 19 h 1Dule . 4 Find the sum of first 20 teams # 3 +8+ 13+18+ . - to Arithmetic progression ( A . P. ) It is a progression only when the difference between the series of numbers in the sequence is the same and of the same interval, when the difference obtained by continously adding a value turns out to be the same , it is Known as a common difference ( d). So, to seek out the nith telm of a progression, We must understand the basic rith teem as In = a + (n-1)d DUS First team = a Second term = atd az as Q4 Third term = a + 2d a atd a+ 2d a +3d - . Fourty term = Q + 3 d a + (n - 1 )d nth Term = at (n- 1 )d where , a, = first team an Q1 = Second term Sum of Series : a an = with team Sn + a2 + as + + anSn = a, + (atd ) + ( a+ 2d) +..... + (a + (n-1)d) . similarly consider an arithmetic progression starting from last telm and going till lateem , that is ( decreasing) flist A.P. for example meaning 3 8+ 10+ 12 = 12+ 10+8 Su = at (m-old + a + (-2)d + ath-3)d + .. + a 2 Add the two equations and 2 , we have. 2 Sn = at atin-old +, atd + ath-2)d, + a + 2d + a + (n- 3) d + + a + (n- 1)d + a, 2 Sn = 2 a + (n-1)d, + , 2 a + (n- 2+ 1)d, +, 20 + ( n- 3 + 2 )d, + 2 a + (n-1)d, 2 Su = n [ za + (n-1)d] as this teem will come n times ) Sn = ~ [ 20 + ( n-1)d ] To find Sum of any AP we can wre this Also, last term ( 1 ) = a + (n-1)d Sn = n at a + ( n-1)d] - " [a + ( a + (- 1)d ) ] Su = n ( a + e )