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14.1 Arithmetic Sequences

14.1 Arithmetic Sequences. OBJ: • Find terms of arithmetic sequences. Arithmetic progressions or sequences (A.P.) have a common difference d between each term. To find d , take any term minus the term before it. Answer 3+2  5 – 3 = 2  5 A.P. Reason d = 2  5

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14.1 Arithmetic Sequences

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  1. 14.1 Arithmetic Sequences OBJ: • Find terms of arithmetic sequences

  2. Arithmetic progressions or sequences (A.P.) have a common differenced between each term. To find d, take any term minus the term before it.

  3. Answer 3+25 – 3 = 25 A.P. Reason d = 25 3+25 + 25 = 3+45 EX:  For each progression that is an A.P., find the common difference d. Give a reason for each answer. 3,3+25, 3+45,…

  4. Answer .2 – -1.3 = 1.5 A.P. Reason d = 1.5 -4.3 + 1.5 = -2.8 EX:  For each progression that is an A.P., find the common difference d. Give a reason for each answer. -4.3,-2.8,-1.3, .2,…

  5. Answer 4.4 – 6.2 = -1.8 A.P. Reason d = -1.8  4.4 + -1.8 = 2.6 EX:  For each progression that is an A.P., find the common difference d. Give a reason for each answer. 6.2, 4.4, 2.6, 0.8,…

  6. Answer Not A.P. Reason 10 – 5 ≠ 20 – 10 EX:  For each progression that is an A.P., find the common difference d. Give a reason for each answer. 5, 10, 20, 40, . . .

  7. Write the next three terms of the A.P.: 1, 1, 7, 5, . . . 8 2 8 4 4 – 1 • 8 3 8 10 8 13 8 16 8 (or 2) 19 8

  8. Write the first four terms of the A.P. whose first term a is 7.5 and common difference d = -3. 7.5 – 3 4.5 – 3 1.5 – 3 -1.5

  9. Find the 36th term of 14, 10, 6, 2,… 10 – 14 = -4 14 + 35(-4) 14 – 140 -126 Find the 26th term of 8, 5.4, 2.8, 0.2,… 5.4 – 8 = -2.6 8 + 25(-2.6) = 8 – 65 = -57 The nth term of an arithmetic progression or sequence is given by the formula: l = a + (n – 1) d

  10. The nth term of an arithmetic progression or sequence is given by the formula: l = a + (n – 1) d Find the 31st term of 3-2,1,-1+2,... -1+2 – 1 = -2+2 = 3-2 + 30(-2 + 2) = 3-2 – 60 + 302) = -57 + 292

  11. 14.4 Geometric Sequences OBJ: • Find terms of geometric sequences

  12. Geometric progressions or sequences (G.P.) have a common ratior between each term To find r, take any term divided by the term before it.

  13. Answer 52 5 2 G.P. Reason r = 2  52 •2 = 10 EX:  For each progression that is an G.P., find the common ratio r. Give a reason for each answer. 5, 52, 10, 102,...

  14. Answer 4 -8 -1 2 Reason r = -1 2  4 • -1 2 = -2 EX:  For each progression that is an G.P., find the common ratio r. Give a reason for each answer. -8, 4, -2, 1,…

  15. Answer -6 -2 = 3 Reason r = 3 -6 • 3 -18 EX:  For each progression that is an G.P., find the common ratio r. Give a reason for each answer. -2, -6, -18, -54,…

  16. Answer 8≠ 6 6 4 Not G.P. Reason Is an A.P. (d = 2) EX:  For each progression that is an G.P., find the common ratio r. Give a reason for each answer. 2, 4, 6, 8, . . .

  17. Answer .6 3 = .2 Reason r = .2 .6 • .2 = .12 EX:  For each progression that is an G.P., find the common ratio r. Give a reason for each answer.3, .6, .12, .024, . . .

  18. Write the next three terms of theG.P.: -1, 1, -1, 1, . . .27 9 3 1 9_ -1 27 1• -27 9 -3 1• -3 -3 • -3 9 • -3 -27

  19. Write the first four terms of the G.P. whose first term a is 0.04 and common ratio r = -10. .04 • -10 -.4 • -10 4 • -10 -40

  20. EX:  7th term: a = 1 and r = -2 8 1 (-2)6 8 1(64) 8 8 Find the 10th term of the G.P.: 1, -1, 2, -4, . . . 2 1 (-2)9 2 1 (-512) 2 -256 The nth term of an geometric progression or sequence is given by the formula: l = a•rn – 1

  21. The nth term of an geometric progression or sequence is given by the formula: l = a•rn – 1 Find the 10th term of the G. P.: 64, -32, 16, -8, … 64 (-1/2)9 64 • -1_ 512 -1_ 8

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