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Sum of an Arithmetic Series
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11.2 – Arithmetic SeriesSum of Arithmetic Sequences
DefinitionsSequence
Series
30,26,22,18ia
30262218
Sum of an Arithmetic SeriesThe sum of the first terms of an arithmetic
series is given by
2)( 1 n
naanS
Example – Sum of an Arithmetic SeriesSum of the first 100 positive integers.
2)( 1 n
naanS
Example – Sum of an Arithmetic SeriesSum of the first 100 positive integers.
2)( 1 n
naanS
100n
Example – Sum of an Arithmetic SeriesSum of the first 100 positive integers.
2)( 1 n
naanS
100n11 a
Example – Sum of an Arithmetic SeriesSum of the first 100 positive integers.
2)( 1 n
naanS
100n11 a100100 a
Example – Sum of an Arithmetic SeriesSum of the first 100 positive integers.
2)( 1 n
naanS
100n11 a100100 a
2)1001(100
100
S
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
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
Example – Find the first three termsWhat are the first three terms of the
arithmetic series in which
Example – Find the first three termsWhat are the first three terms of the
arithmetic series in which
2)( 1 n
naanS
dnaan )1(1
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
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
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
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
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
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
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
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
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
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
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
Assignment
Assignment
State whether each statement is true or false. Explain.