OBJ: • Find terms of arithmetic sequences

Arithmetic progressions or sequences (A. P 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 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,… 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 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 = 1.5 A.P. Reason d = 1.5  -4.3 + 1.5 = -2.8

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

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

Write the first four terms of the A. P. whose first term a is 7 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

The nth term of an arithmetic progression or sequence is given by the formula: l = a + (n – 1) d 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 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

OBJ: • Find terms of geometric sequences

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

EX:  For each progression that is an G. P. , find the common ratio r 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,... 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 EX:  For each progression that is an G.P., find the common ratio r. Give a reason for each answer. -8, 4, -2, 1,… 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 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 = 3 Reason r = 3 -6 • 3 -18

EX:  For each progression that is an G. P. , find the common ratio r 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 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 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 = .2 Reason r = .2 .6 • .2 = .12

Write the next three terms of the G.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 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 – 1 Find the 10th term of the G.P.: 1, -1, 2, -4, . . . 2 1 (-2)9 1 (-512) -256 EX:  7th term: a = 1 and r = -2 8 1 (-2)6 1 (64)

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