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UNIT
8 :
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, …}
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: