Arithmetic Sequences.

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Presentation transcript:

Arithmetic Sequences

A sequence in which a constant (d) can be added to each term to get the next term is called an Arithmetic Sequence. The constant (d) is called the Definition Common Difference. To find the common difference (d), subtract any term from one that follows it. t1 t2 t3 t4 t5 2 5 8 11 14 3 3 3 3

Find the first term and the common difference of each arithmetic sequence. Examples: First term (a): 4 Common difference (d): = 9 – 4 = 5 First term (a): 34 Common difference (d): -7 BE CAREFUL: ALWAYS CHECK TO MAKE SURE THE DIFFERENCE IS THE SAME BETWEEN EACH TERM !

Now you try! Find the first term and the common difference of each of these arithmetic sequences. a) 1, -4, -9, -14, …. b) 11, 23, 35, 47, …. c) 3, 9, 15, 21…….. d) 2x, 7x, 12x,……...

Word Problem A school sets a fine of P30.00 for the first littering offense. The fine increases by P5.00 for each subsequent offense. How much will a student be fined for the tenth offense?

What is the 90th term of the sequence 30, 35, 40, 45? Try this! What is the 90th term of the sequence 30, 35, 40, 45?

The first term of an arithmetic sequence is (a) The first term of an arithmetic sequence is (a) . We add (d) to get the next term. There is a pattern, therefore there is a formula we can use to give use any term that we need without listing the whole sequence . 3, 7, 11, 15, …. We know a = 3 and d = 4 t1= a = 3 t2= a+d = 3+4 = 7 t3= a+d+d = a+2d = 3+2(4) = 11 t4 = a+d+d+d = a+3d = 3+3(4) = 15

The first term of an arithmetic sequence is (a) The first term of an arithmetic sequence is (a) . We add (d) to get the next term. There is a pattern, therefore there is a formula we can use to give use any term that we need without listing the whole sequence . The nth term of an arithmetic sequence is given by: tn = a + (n – 1) d The last # in the sequence/or the # you are looking for The position the term is in First term The common difference

The 14th term in this sequence is the number 43! Examples: Find the 14th term of the arithmetic sequence 4, 7, 10, 13,…… tn = a + (n – 1) d You are looking for the term! t14 = The 14th term in this sequence is the number 43!

The 14th term in this sequence is the number -73! Examples: Find the 14th term of the arithmetic sequence with first term of 5 and the common difference is –6. a = 5 and d = -6 You are looking for the term! List which variables from the general term are provided! tn = a + (n – 1) d t14 = -6 5 = 5 + (13) * -6 = 5 + -78 = -73 The 14th term in this sequence is the number -73!

The 100th term in this sequence is 301! Examples: In the arithmetic sequence 4,7,10,13,…, which term has a value of 301? tn = a + (n – 1) d You are looking for n! The 100th term in this sequence is 301!

Find the 67th term of the sequence 1, 5, 9, 13. Board Drill Find the 67th term of the sequence 1, 5, 9, 13.

In the sequence50, 45, 40, 35,…. Which term is 5? Board Drill In the sequence50, 45, 40, 35,…. Which term is 5?

Board Drill The 16th term of the arithmetic sequence is 48. If the common difference is 3, find the first term.

Seatwork No. 1 Write the first six terms of the arithmetic sequence from the given data. 1. a1 = 1 ; d = 1 2. a1 = 15 ; d = 3 3. a1 = -18 ; d = 7 4. a1 = 2 ; d = 4 5. a1 = 1/6 ; d = 1/2

6. Find the 11th term in the sequence 3, 4, 5… 7 6. Find the 11th term in the sequence 3, 4, 5… 7. Find the 20th term in the sequence 17, 13, 9… 8. Find the last term of the sequence 5, 10, 15,…..to 42 terms. 9. If a1 = 5, an = 395 and d = 5, find the value of n. 10. If a1 = 5, a7 = 17 and n= 7, find the common difference.