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Transcript 
Arithmetic and Geometric
sequence and series
Definitions
A sequence is a list of numbers which follow a definite pattern
or rule.
• If the rule is that each term, after the first, is obtained by
adding a constant, d, to the previous term, then the sequence
is called an arithmetic sequence, such as 2, 6, 10, 14, 18, 22, .
. . , where d — 4. d is known as the common difference.
• If the rule is that each term, after the first, is obtained by
multiplying the previous term by a constant, r, then the
sequence is called a geometric sequence, such as, 4, 16, 64,
256, 1024, where r = 4. r is known as the common ratio.
A series is the sum of the terms of a sequence.
• A series is finite if it is the sum of a finite number of terms of
a sequence.
• A series is infinite if it is the sum of an infinite number of
terms of a sequence.
EXAMPLE
• An arithmetic series is the sum of the terms of an
arithmetic sequence, such as 2, 6, 10, 14, 18, 22, . . . ,
with d= 4
• Find the sum of the first 15 terms of the series:
20+18+16+14 +
• Solution
• This is an arithmetic series since the difference d = -2.
Therefore, a = 20, d = –2, n = 15, and hence, using
formula
• S15=15/2[2(20) + (15-l)(-2)]
• = 90
Exercises Simple and Compound
Interest
1. Suppose £5000 is invested for five years. Calculate the amount
accumulated at the end of five years if interest is compounded
annually at a nominal rate of (a) 5%, (b) 7%, (c) 10%.
2. A savings account of £10000 earns simple interest at 5% per annum.
Calculate the value of the account (future value) after six years.
3. £2500 is invested at a nominal rate of interest of 5% per annum.
Calculate the amount accumulated at the end of (a) 1 year, (b) 4.5
years, (c) 10 years, (d) 20 years.
4. Calculate the present value of £6000 that is expected to be received
in three years' time with simple interest of 7.5% per annum.
5. How much is a sum £3500 worth at the end of five years if deposited
at (a) 11 % simple interest and (b) 11 % compound interest, each
calculated annually?
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