ARITHMETIC SEQUENCE

Prepared by:

Mr. Junaz S. Emboy

OBJECTIVES

*Define and identify an arithmetic sequence

*Give the formula for the nth term of an arithmetic sequence

*Solve an arithmetic sequence

Review

Sequence-a sequence is a succession of number in a specific order.

Examples2, 4, 6, 8, 10, 12, …

3, 9, 27, 81, 243 …

Let’s Try This!By following the pattern, give the next three terms of the sequence;

1.) 1, 2, 3, 4, 5, 1.) 1, 2, 3, 4, 5, 6, 7, 8

2.) 2, 5, 8, 11, _ 2.) 2, 5, 8, 11, 14, 17, 20

5.) 1, 4, 16, 64,

3.) 5, 10, 15, 20, 25, 30, 354.) 1, 2, 4, 8, 4.) 1, 2, 4, 8, 16, 32, 645.) 1, 4, 16, 64, 256, 1024, 4096

3.) 5, 10, 15, 20,

Arithmetic Sequence

-an arithmetic sequence is a sequence in which the difference between any two consecutive terms is the same.

Let’s Identify

1.) 1, 2, 3, 4, 5, 6, 7, 82.) 2, 5, 8, 11, 14, 17, 20

3.) 1, 4, 16, 64, 256, 1024, 4096

4.) 5, 10, 15, 20, 25, 30, 35

5.) 1, 2, 4, 8, 16, 32, 64

Identify which is/are arithmetic sequence and which is/are not arithmetic sequence of the following sequence.

Arithmetic SequenceArithmetic Sequence

Arithmetic Sequence

Not

Not

By pattern searching, identify the 10th term of the following.1.) 1, 2, 3, 4, 5, 6, 7, 8

2.) 2, 5, 8, 11, 14, 17, 20

10th term is 10

10th term is 29

Just add 1 to the preceding term1 is called the common difference (d) and is obtained by subtracting the 2nd term by the 1st term, 3rd term by the 2nd term and so on.

Just add 3 to the preceding term

Note that the sequence 1, 2, 3, 4, 5, 6, 7, 8 with the common difference 1 can be expressed as1, 1+1, 2+1, 3 + 1, 4 + 1, 5 + 1, 6 + 1, 7 + 1, 8 + 1

In general, the sequencea1 , a2 , a3 , a4 , a5 ,…, an

with a common difference can be expressed as

a1 , a1 + d, a1 + 2d, a1 + 3d, … a1 + (n-1)dNote that the last term is a1 + (n-1)d. Thus,an = a1 + (n-1) d

where, a1 is the first terman is the last termn is the number of terms d is the common difference

Solve for the 10th term using the formula an = a1 + (n-1) d

1.) 1, 2, 3, 4, 5, 6, 7, 8 2.) 2, 5, 8, 11, 14, 17, 20Given: a1 =1, d = 1, n=10

a10 = a1 + (n-1) d = 1 + (10-1) 1 = 1 + (9)1 = 1 + 10a10 = 10

Given: a1 =2, d = 3, n=10

a10 = a1 + (n-1) d = 2 + (10-1) 3 = 2 + (9)3 = 2 + 27a10 = 29

Practice ExercisesIdentify whether each sequence is arithmetic or not. If it is, find the common difference and solve for the 11th term.1.) 7, 10, 13, 16, …2.) 9, 11, 13, 15, …3.) 4, 12, 36, 108, …

Identify the common difference and solve for the next three terms of the ff arithmetic sequence.

4.) 6, 12, 18, _, _, _5.) 28, 25, 23, _, _, _

Identify whether each sequence is arithmetic or not. If it is, find the common difference and solve for the 11th term.1.) 7, 10, 13, 16, …Arithmetic Sequence

2.) 9, 11, 13, 15, …

3.) 4, 12, 36, 108, …

Given: a1 =7, d = 3, n=11an = a1 + (n-1) d = 7 + (11-1) 3 = 7 + (10)3 = 7 + 30a11 = 37

Arithmetic SequenceGiven: a1 =9, d = 2, n=11an = a1 + (n-1) d = 9 + (11-1) 2 = 9 + (10)2 = 9 + 20a11 = 29

Not Arithmetic Sequence

Identify the common difference and solve for the next three terms of the ff arithmetic sequence.4.) 6, 12, 18, 24, 30, 36

5.) 28, 25, 23, 20, 17, 14

4.) 6, 12, 18,

5.) 28, 25, 23,

d = 12 – 6 d = 18 – 12 = 6 = 6

Just add 6 to the preceding term to get the next 3 terms

Just add -3 to the preceding term to get the next 3 terms

d = 25 – 28 d = 23 – 25 = -3 = -3

Group ActivityQuestion: What is the other term of the word sequence?Clue: Solve each problem. Each answer corresponds to the ordinal number of each letter of the alphabet -- that is A=1, B=2, C=3, …, Z=26.Remember: Show your solution if necessary. Every member of the group should help in finding the solutions to the problems.

Questions

Solve for the first six terms of the arithmetic sequence given that;1.) a1 = 2 and d = 32.) a1 = 1/6 and d = 1/3

EVALUATION

Identify whether each sequence is arithmetic or not. If it is, find the common difference and solve for the 15th term.3.) 20, 6, 3, 1 ½, …4.) 32, 35, 38, …5.) 1/3, 2/3, 1, …

ASSIGNMENT

Find the common difference and solve for the term required in the following arithmetic

sequence.a. the 6th term of 2, 6, 10, …b. the 7th term of 2, 11, 20,…c. the 8th term of 9, 6, 3, …