Arithmetic Sequences and Series Sequences and Series Preliminary Maths

Transcription

1 Arithmetic Sequeces ad Series Arithmetic Sequeces ad Series Sequeces ad Series Prelimiary Maths

2 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 arithmetic sequeces ad series

3 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

4 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 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? arithmetic sequeces ad series

5 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 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 Evaluate 3i 40 i18 Questio 6 0 Evaluate 3i i18 arithmetic sequeces ad series

6 Arithmetic Sequeces ad Series Sequeces ad Series 5 Fully Worked Solutios Questio 1 (a) a5 ad d 35 T a 1 d T (b) T a d 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 T 6 19 (b) T Questio 3 (a) T a d 13 1 T5 a 4d d 18, that is d 6 substitute 6 ad 13 1 d ito a 6 13, that is a 7 T a 1 d T 6 1 (b) T 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) T Questio 5 (a) a5. ad d. arithmetic sequeces ad series

7 6 Arithmetic Sequeces ad Series Sequeces ad Series T T. 3 (b) T , 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 (b) T Questio 8 T 1 44 thus terms Questio 9 (a) T4 a 3d 116 a a 89 (b) T30 a 9d Questio 10 (a) a 48 ad d 7 T T 55 7 (b) Questio 11 a 7 ad d T a 1 d Questio 1 arithmetic sequeces ad series

8 Arithmetic Sequeces ad Series Sequeces ad Series 7 a 15, d 4, 1 1 S $ $4 $444 0 Questio 13 a S a 1 d 1 1 Questio 15 Questio S T50 a 1, d, S Questio 16 a Questio 17 0 $10 1 $95 Questio cm Questio $00 1 $1150 Questio 0 S 100, S a 10 1 d 100 a9d a 0 1 d 400 a19d d 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 T S0 a Questio a 3 ad d 4 S arithmetic sequeces ad series

9 8 Arithmetic Sequeces ad Series Sequeces ad Series or 10 but must be a positive umber, thus 10 Questio 3 (a) a7d 16 1 a1d d 65, that is d 13 substitute 13 a7d 16 1 d ito a , that is a 75 a 75 ad d 13 5 S (b) Questio 4 4 i1 0 Questio 5 i Questio 6 i18 0 i18 i i arithmetic sequeces ad series

10 Arithmetic Sequeces ad Series Sequeces ad Series arithmetic sequeces ad series