What is a Series? A series is the sum of terms of a sequence.
The sum of the first n terms in a sequence is denoted as S n. S 5
the sum of the first 5 terms
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Arithmetic Series Recall: A sequence like 2, 5, 8, 11,, is
called an arithmetic sequence with a = 2 and d = 3. Therefore a
series that corresponds to this arithmetic sequence is 2 + 5 + 8 +
11 +, is called an arithmetic series.
Slide 5
Arithmetic Series Formula The Sum of the First n terms of an
Arithmetic Series Recall: Arithmetic Sequence formula Rewrite this
series in reverse order Add this two rows together There are n
terms in total Formula 1 or a +(n - 1)d Formula 2
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Example 1 Sum of a Series given the first term Find the sum of
the first 60 terms of each series.
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Example 2 Sum of a series given first and last terms Find the
sum of the arithmetic series 5 + 9 + 13 +... + 201. 50 There are 50
terms in the series. 50
Slide 8
Example 3 Word Problem A student is offered a job with a math
teacher that will last 20 hours. The first option pays $4.75 for
the first hour, $5 for the second hour, $5.25 for the next hour,
and so on. The second option pays $7/h for all hours worked. Which
option pays more? 20 The amount earned by the first option is
$142.50. The amount earned by the second option is $7 x 20 = $140.
So, the first option pays more. 20
