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Arithmetic Sequences

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 UNIT 10 : SEQUENCES AND SERIES

 LESSON 1: ARITHMETIC SEQUENCES

 

 

Arithmetic Sequences:

A sequence such as 2, 3, 8, 13, is called an Arithmetic Sequence. These sequences have the following properties.

        Terms are denoted as t1 , t2 , t3 , referring to term1, term 2, term 3

        The difference between successive terms is constant. ie t2 t1 = t3 t2 = t4 t3 etc

        This difference is called the common difference and denoted using the letter d. Here d = 5.

        The first term is denoted using the letter a. Here a = -2.

        Successive terms are found by adding the common difference, d, to the preceding term. Hence t5 = 13 + 5 = 18 etc.

        The formula for the general term or nth term is tn = a + (n 1)d

        Arithmetic sequences are linear functions with domain the natural numbers N = {1, 2, 3, 4, 5, }

Text Box: a = t1 = first term
d = common difference
n = term number
tn = nth term or general term
 

 

 

 

 

 

 

 


Example 1:

For the arithmetic sequence above, find t7, t11 and the general term tn.

 

Solution:

a = -2

d = 5

n = 7, 11, n

 

 

 

Example 2: Finding specific terms and the General (nth) Term.

Given the sequence 3, -7, -11, -15,

a) Show that the sequence is arithmetic.

b) Find t7, t11 and the general term tn.

 

Solution:

 

a = - 3

d = - 4

n = 7, 11, n

 

 

 

 

 

 

 


Example 3: Finding the Number of Terms in a Given Sequence.

Given the sequence 4, 1, -2, , -65. Find the number of terms in the sequence.

Solution:

Let the last term be tn.

a = 4

d = - 3

n = ?

tn = - 65

 

 

 

 

 

 

 

 

 

 

 

 


Example 4: Solving a Sequence given two terms.

The fourth and seventh terms of an arithmetic sequence are 8 and 17 respectively. Find a, d and tn

Solution:

 

 

 

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