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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 - PowerPoint PPT Presentation

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.

EX: For each progression that is an A.P., find the common difference d. Give a reason for each answer. 3,3+25, 3+45,

Answer3+25 3 = 25 A.P.Reasond = 25 3+25 + 25 = 3+45

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,

Answer.2 -1.3 =1.5A.P.

Reasond = 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. 6.2, 4.4, 2.6, 0.8,

Answer4.4 6.2 =-1.8A.P.Reasond = -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. 5, 10, 20, 40, . . .

AnswerNot A.P.Reason10 5 20 10

Write the next three terms of the A.P.: 1, 1, 7, 5, . . . 8 2 8 4 4 1 8 38

10 813 816 8 (or 2)19 8

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

7.5 34.5 31.5 3-1.5

The nth term of an arithmetic progression or sequence is given by the formula: l = a + (n 1) dFind the 36th term of14, 10, 6, 2,10 14 = -414 + 35(-4)14 140-126Find the 26th term of8, 5.4, 2.8, 0.2,5.4 8 = -2.68 + 25(-2.6) =8 65 =-57

The nth term of an arithmetic progression or sequence is given by the formula: l = a + (n 1) dFind the 31st term of 3-2,1,-1+2,...-1+2 1 =-2+2 =3-2 + 30(-2 + 2) =3-2 60 + 302) =-57 + 292

14.4 Geometric Sequences

OBJ: Find terms of geometric sequences

Geometric progressions or sequences (G.P.) have a common ratio r between each term

To find r, take any term divided by theterm before it.

EX: For each progression that is an G.P., find the common ratio r. Give a reason for each answer. 5, 52, 10, 102,...

Answer5252G.P.

Reasonr = 2 52 2 =10

EX: For each progression that is an G.P., find the common ratio r. Give a reason for each answer. -8, 4, -2, 1,

Answer4-8-1 2Reasonr = -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. -2, -6, -18, -54,

Answer-6-2 =3Reasonr = 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, 4, 6, 8, . . .

Answer 8 6 6 4Not G.P.

ReasonIs 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. 3, .6, .12, .024, . . .Answer.6 3 =.2Reasonr = .2.6 .2 =.12

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

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

The nth term of an geometric progression or sequence is given by the formula: l = a rn 1EX: 7th term:a = 1 and r = -2 8 1 (-2)6 8 1 (64) 88

Find the 10th term ofthe 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 1Find the 10th term of the G. P.:64, -32, 16, -8, 64 (-1/2)964 -1_ 512 -1_ 8