1. CHAPTER 1 ARITHMETIC AND GEOMETRIC SEQUENCES
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CHAPTER 1
ARITHMETIC
AND
GEOMETRIC SEQUENCES
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BUSINESS MATHEMATICS

2. 1.1 SEQUENCE (PROGRESSION)
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1.1 SEQUENCE (PROGRESSION)
A list of numbers arranged in a specified order.
Two sequences namely:
- arithmetic
- geometric
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3. Arithmetic sequence Common difference (a) 4, 8, 12, 16, …… 4
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1.2 ARITHMETIC SEQUENCE
One in which the difference between any term and the preceding term is the same throughout.
Example:
Arithmetic sequence Common difference
(a) 4, 8, 12, 16, …… 4
(b) ½, 1, 1½, 2, …… ½
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4. 1.3 Nth TERM AND SUM OF FIRST N TERMS OF AN ARITHMETIC SEQUENCE
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1.3 Nth TERM AND SUM OF FIRST N TERMS OF AN ARITHMETIC SEQUENCE
If first term of an arithmetic sequence is a and common difference is d, then the arithmetic sequence is written as:
a, a + d, a + 2d, a + 3d, ……
To find the nth term:
Tn = a + (n – 1)d
where:
Tn = nth term
a = first term
n = number of terms
d = common difference
Sn = n/2 [2a + (n-1)d]
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1.4 GEOMETRIC SEQUENCE
A sequence of numbers and the ratio between any term. It is obtained by multiplying the first term by the ratio to get the second term and so on.
The ratio is known as common ratio and can be obtained by dividing any term by the term before it.
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6. Geometric sequence Common ratio (r)
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Example:
Geometric sequence Common ratio (r)
(a) 1, 2, 4, 8, 16, 32, …… (4/2) or (8/4)
-3, 6, -12, 24, …… (6/-3) or (-12/6)
0.1, 0.01, 0.001, …… (0.01/0.1)
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7. 1.5 Nth TERM AND SUM OF FIRST N TERMS OF A GEOMETRIC SEQUENCE
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1.5 Nth TERM AND SUM OF FIRST N TERMS OF A GEOMETRIC SEQUENCE
If a geometric sequence is a, ar, ar2, ar3, ……, arn-1, thus:
Tn = arn-1
Sn = a(1 – rn) / (1 – r) for r < 1
Sn = a(rn - 1) / (r – 1) for r > 1
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