Arithmetic Sequence
- 1. Prepared by: Kevin P. Gabisay Joan C. Tonacao Jezreel A. Carbonquillo Arithmetic Sequence
- 2. Learning Objectives: I can identify arithmetic sequences I can calculate the nth term in arithmetic sequences I can find the number of terms in an arithmetic sequences
- 3. Arithmetic Sequence -is a sequence where each new term after the first is obtained by adding a constant d, to the preceding term. Identifying an Arithmetic Sequence Sequences of numbers that follow a pattern of adding a fixed number from one term to the next are called arithmetic sequences. The following sequences are arithmetic sequences: Example A: 5 , 8 , 11 , 14 , 17 , ... For Example A, if we add 3 to the first number we will get the second number. This works for any pair of consecutive numbers. The second number plus 3 is the third number: 8 + 3 = 11, and so on.
- 4. Example B: Write down the first 5 term of arithmetic sequence with first term 8 and common difference of 7. Answer: 8, 15, 22, 29, 36 Because this sequence behave according to this simple rule of adding a constant number to one term to get to another, they are called arithmetic sequence. So that we can examine these sequence to greater depth, we must know that the fixed numbers that bind each sequence together are called the common difference. Sometimes mathematicians use the letter d when referring to these types of sequence.
- 5. Calculating the nth Term The formula for finding any term of an arithmetic sequence is an=a+ (n-1)d where a is the first term of the sequence, d is the common difference, and n is the number of the term to find.
- 6. EXAMPLE: Last February, Sharon Cuneta held a mega-concert at the Coliseum. How many chairs are in the Coliseum if there are 40 rows and the first row contains 200 seats and the second row contains 250 seats and the succeeding rows follow this arithmetic sequence? Given: a1 = 200, an = 40, d = 50 Ask: How many seats contains by the last row? Formula: an= a1 + (n-1) d a40 = 200 + (40-1) 50 a40 = 200 + (39) 50 a40 = 200 + 1950 a40 = 2150
- 7. There is also another formula to use: an = dn + the number before the first term where: d – is the difference between the first term an/n – the term that is ask to find out Base on the given problem: Given: a1 = 200, an /n = 40, d = 50 Formula: an = dn + the number before the first term a40 = 50 (40) + 150 a40 = 2000 + 150 a40 = 2150
- 8. Evaluation: Direction: Solve what is ask? 1. Write down the 50th and 60th terms of arithmetic sequence 7,15,23,… 2. Find the sum of all integers from 1 to 1,000. 3. Find the sum of the first 100 terms of even integers. 4. Write down the 101th term of arithmetic sequence 2/15,7/15,12/15,… 5. An arithmetic sequence has first term 4 with the difference of ½. Find the sum of first 120 terms.
- 9. References: http://www.mathguide.com/lessons/SequenceArithmeti c.html Exploring Mathematics II (Intermediate Algebra), by Orlando A. Oronce and Marilyn O. Mendoza