sum of arithmetic sequences. definitions sequence series

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.