Arithmetic Sequeces ad Series Arithmetic Sequeces ad Series Sequeces ad Series Prelimiary Maths www.primeeducatio.com.au
Arithmetic Sequeces ad Series Sequeces ad Series 1 Questio 1 The first 5 terms of a arithmetic sequece are 5, 40, 75, 110, 145. (a) Write dow the rule for the arithmetic sequece. (b) Fid the 0 th term. 1 Questio The third term of a arithmetic sequece is -1 ad the fifth term is 11. (a) Write dow the rule for the arithmetic sequece. (b) Fid the 50 th term of the sequece. 1 Questio 3 The d term of a arithmetic sequece is 13 ad the 5 th term is 31. (a) Write dow the rule for the arithmetic sequece. (b) Fid the 17 th term of this sequece. 1 Questio 4 The d term of a arithmetic sequece is 0 ad the 6 th term is -8. (a) Write dow the rule for the arithmetic sequece. (b) Fid the 3 d term of this sequece. 1 Questio 5 The first three terms of a arithmetic sequece are 5., 7.4 ad 9.6. (a) Write dow the rule for the arithmetic sequece. (b) Fid which term is equal to 53.6. 1 www.primeeducatio.com.au arithmetic sequeces ad series
Arithmetic Sequeces ad Series Sequeces ad Series Questio 6 Cosider a arithmetic sequece, x 3 y, 3x 7 y, 4x 11 y,. (a) Write dow the rule for the arithmetic sequece. (b) Fid 8 th term. 1 Questio 7 The 5 th term of a arithmetic sequece is 13 ad the 9 th term is 5. (a) Write dow the rule for the arithmetic sequece. (b) Fid the 50 th term. 1 Questio 8 Fid the umber of terms i a arithmetic sequece with the first term, the commo 3 differece ad the last term 44. Questio 9 The fourth term of a arithmetic sequece is 116 ad the commo differece is 9. (a) Fid the first term. 1 (b) Fid the 30 th term. 1 Questio 10 The first three terms of a arithmetic sequece are 48, 41, 34. (a) Write dow a formula for the th term. (b) If the last term of the sequece is -9, how may terms are there i the sequece? 1 Questio 11 Fid the first value of for which the sequece 7, 5, 3, becomes egative. arithmetic sequeces ad series www.primeeducatio.com.au
Arithmetic Sequeces ad Series Sequeces ad Series 3 Questio 1 Jessica saves $15 i the first week, $19 i the secod week, $3 i the third week ad cotiues to icrease her savigs each week by the same amout util the twelfth week. How much is she the savig i total? Questio 13 Fid the sum of 0 terms of a arithmetic series if the first term is 9 ad the last term is 99. Questio 14 Fid the sum of the first umbers of the series 13 57. Questio 15 Fid the sum of the first 50 odd umbers. 3 Questio 16 The th term of a arithmetic sequece is T 3 1. Fid the sum of 40 terms. Questio 17 A boy ears $10 the first week ad 50 cets more each week tha i the precedig week. What is the total sum of moey he ears i 0 weeks? Questio 18 A ball, rollig dow a slope, rolls 16 cm i the first secod, 48 cm i the d secod, 80 cm i the third secod ad so o. At this rate how far will it roll i 8 secods? Questio 19 A drill test costs $00 for the first 10 metres, $50 for the ext 10 metres, $300 for the ext 10 metres ad so o. What will the drillig cost for a depth of 180 metres? www.primeeducatio.com.au arithmetic sequeces ad series
4 Arithmetic Sequeces ad Series Sequeces ad Series Questio 0 The sum of the first 10 terms of a arithmetic series is 100 ad the sum of the ext 10 terms is 300. Fid the first term ad the commo differece. Questio 1 Fid the sum to 0 terms of the arithmetic series whose th term is 3 1. Questio How may terms of the series 3 19 15 11 must be added to give a sum of 50? Questio 3 The 8 th term of a arithmetic sequece is 16 ad the 13 th term is 81. (a) Fid the first term ad the commo differece. (b) Fid the sum of the first 5 terms. 1 Questio 4 Evaluate 4 i. 1 i1 Questio 5 0. 1 Evaluate 3i 40 i18 Questio 6 0 Evaluate 3i 40. 1 i18 arithmetic sequeces ad series www.primeeducatio.com.au
Arithmetic Sequeces ad Series Sequeces ad Series 5 Fully Worked Solutios Questio 1 (a) a5 ad d 35 T a 1 d 5 1 35 5 35 35 35 30 T 35 30 (b) T a d 0 1 5 0 1 35 670 Questio (a) T3 a d 1 1 T5 a 4d 11 1 d1, that is d 6 substitute 6 d ito ad 1 1 a 6 1, that is a 13 T a 1 d 13 1 6 13 6 6 6 19 T 6 19 (b) T50 650 19 81 Questio 3 (a) T a d 13 1 T5 a 4d 31 1 3d 18, that is d 6 substitute 6 ad 13 1 d ito a 6 13, that is a 7 T a 1 d 7 1 6 7 6 6 6 1 T 6 1 (b) T17 617 1 103 Questio 4 (a) T a d 0 1 T6 a 5d 8 1 4d 8, that is d substitute d ito ad 0 1 a 0, that is a T a 1 d 1 4 T 4 (b) T3 3 4 60 Questio 5 (a) a5. ad d. www.primeeducatio.com.au arithmetic sequeces ad series
6 Arithmetic Sequeces ad Series Sequeces ad Series T 5. 1. 5.... 3 T. 3 (b) T. 3 53.6. 53.6 3 50.6, that is 3 Questio 6 (a) a x 3 y ad d x 4y T x 3y 1 x 4y x 3y x 4y x 4y x 4y x y 4 (b) T x y x y T8 x 4y 8 x y 8x 3y x y 9x 31y Questio 7 (a) T5 a 4d 13 1 T9 a 8d 5 1 4d 1, that is d 3 substitute 3 a4d 13 1 d ito a 43 13, that is a 1 T 1 1 3 3 (b) T50 350 148 Questio 8 T 1 44 thus terms Questio 9 (a) T4 a 3d 116 a 39 116 a 89 (b) T30 a 9d 89 99 350 Questio 10 (a) a 48 ad d 7 T 48 1 7 48 7 7 55 7 T 55 7 (b) 55 7 9 1 Questio 11 a 7 ad d T a 1 d 7 1 0 9 0 9 114.5 115 Questio 1 arithmetic sequeces ad series www.primeeducatio.com.au
Arithmetic Sequeces ad Series Sequeces ad Series 7 a 15, d 4, 1 1 S $15 1 1 $4 $444 0 Questio 13 a 9 99 1080 S a 1 d 1 1 Questio 15 Questio 14 50 S50 1 3 5 T50 a 1, d, 50 50 S50 1 50 1 500 40 Questio 16 a 4 11 500 Questio 17 0 $10 1 $95 Questio 18 8 16 1 104 cm Questio 19 18 $00 1 $1150 Questio 0 S 100, S 100 300 400 10 0 10 a 10 1 d 100 a9d 0 1 0 a 0 1 d 400 a19d 40 1 10d 0, that is d substitute a9d 0 1 d ito a 9 0, that is a 1 the first term is 1 ad the commo differece is Questio 1 at 1 311 T 0 30 1 59 0 S0 a 59 610 Questio a 3 ad d 4 S 3 14 50 www.primeeducatio.com.au arithmetic sequeces ad series
8 Arithmetic Sequeces ad Series Sequeces ad Series 5 50 0 5 10 0.5 or 10 but must be a positive umber, thus 10 Questio 3 (a) a7d 16 1 a1d 81 1 5d 65, that is d 13 substitute 13 a7d 16 1 d ito a 713 16, that is a 75 a 75 ad d 13 5 S5 75 5 1 13 05 (b) Questio 4 4 i1 0 Questio 5 i Questio 6 i18 0 i18 i 1 3 4 10 3 40 14 17 0 51 3i 40 318 319 30 40 131 arithmetic sequeces ad series www.primeeducatio.com.au
Arithmetic Sequeces ad Series Sequeces ad Series 9 www.primeeducatio.com.au www.primeeducatio.com.au arithmetic sequeces ad series