sum of arithmetic sequences. definitions sequence series
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Sum of an Arithmetic SeriesTRANSCRIPT
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11.2 – Arithmetic SeriesSum of Arithmetic Sequences
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DefinitionsSequence
Series
30,26,22,18ia
30262218
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Sum of an Arithmetic SeriesThe sum of the first terms of an arithmetic
series is given by
2)( 1 n
naanS
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Example – Sum of an Arithmetic SeriesSum of the first 100 positive integers.
2)( 1 n
naanS
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Example – Sum of an Arithmetic SeriesSum of the first 100 positive integers.
2)( 1 n
naanS
100n
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Example – Sum of an Arithmetic SeriesSum of the first 100 positive integers.
2)( 1 n
naanS
100n11 a
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Example – Sum of an Arithmetic SeriesSum of the first 100 positive integers.
2)( 1 n
naanS
100n11 a100100 a
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Example – Sum of an Arithmetic SeriesSum of the first 100 positive integers.
2)( 1 n
naanS
100n11 a100100 a
2)1001(100
100
S
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Example – Sum of an Arithmetic SeriesSum of the first 100 positive integers.
2)( 1 n
naanS
100n11 a100100 a
2)1001(100
100
S
)101(50100 S
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Example – Sum of an Arithmetic SeriesSum of the first 100 positive integers.
2)( 1 n
naanS
100n11 a100100 a
2)1001(100
100
S
)101(50100 S
5050100 S
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Example – Find the first three termsWhat are the first three terms of the
arithmetic series in which
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Example – Find the first three termsWhat are the first three terms of the
arithmetic series in which
2)( 1 n
naanS
dnaan )1(1
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Example – Find the first three termsWhat are the first three terms of the
arithmetic series in which
2)( 1 n
naanS
dnaan )1(1
2)1059(741
n
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Example – Find the first three termsWhat are the first three terms of the
arithmetic series in which
2)( 1 n
naanS
dnaan )1(1
2)1059(741
n
2)114(741 n
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Example – Find the first three termsWhat are the first three terms of the
arithmetic series in which
2)( 1 n
naanS
dnaan )1(1
2)1059(741
n
2)114(741 n
n57741
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Example – Find the first three termsWhat are the first three terms of the
arithmetic series in which
2)( 1 n
naanS
dnaan )1(1
2)1059(741
n
2)114(741 n
n57741
n13
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Example – Find the first three termsWhat are the first three terms of the
arithmetic series in which
2)( 1 n
naanS
dnaan )1(1
2)1059(741
n
2)114(741 n
n57741
n13
daa )113(113
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Example – Find the first three termsWhat are the first three terms of the
arithmetic series in which
2)( 1 n
naanS
dnaan )1(1
2)1059(741
n
2)114(741 n
n57741
n13
daa )113(113
d129105
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Example – Find the first three termsWhat are the first three terms of the
arithmetic series in which
2)( 1 n
naanS
dnaan )1(1
2)1059(741
n
2)114(741 n
n57741
n13
daa )113(113
d129105
d1296
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Example – Find the first three termsWhat are the first three terms of the
arithmetic series in which
2)( 1 n
naanS
dnaan )1(1
2)1059(741
n
2)114(741 n
n57741
n13
daa )113(113
d129105
d1296d8
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Example – Find the first three termsWhat are the first three terms of the
arithmetic series in which
2)( 1 n
naanS
dnaan )1(1
2)1059(741
n
2)114(741 n
n57741
n13
daa )113(113
d129105
d1296d825,17,9
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Additional ExamplesFind the sum of the first 20 even numbers,
beginning with 2.
What are the first four terms of an arithmetic series in which
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Additional ExamplesFind the sum of the first 20 even numbers,
beginning with 2.
What are the first four terms of an arithmetic series in which
420nS
23,20,17,14
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Assignment
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Assignment
State whether each statement is true or false. Explain.