Section 11.2Arithmetic Sequences

IBTWW:

04/21/23

Honors Precalculus

Arithmetic Sequence

nth term of an arithmetic sequence

Sum of the first n terms of an arithmetic sequence

Has a common difference (d) between terms

ex: 1, 4, 7, 10, . . .

1 2, ,1,

3 3

d = 3

1d =

3

1 1na a n d nth

term1st

term

common difference

1

2n

n

a aS n

Sum of n terms

average term

number of terms

1. Find the 50th term of 1,4,7, …

2. Find the first term and the common difference of the arithmetic sequence with 8th term 28 and 5th term 10.

1 1na a n d

50 1 50 1 3a

d = 3

50 1 49 3a

50 1 147a 148

1 1na a n d 8 5

8 5

a ad

28 10

8 5

6

18

3 8 1 8 1 6a a

128 42a

114 a

3. Find the sum of2 + 5 + 8 + . . . + 41

d = 3

1a 21

2n

n

a aS n

2 41

2nS n

na 41

1 1na a n d 41 2 1 3n

41 3 1n 42 3n14 n

14 21.5 14S

14 301S

Section 11.2Arithmetic Sequences

IBTWW:

Honors Precalculus

Arithmetic Sequence

nth term of an arithmetic sequence

Sum of the first n terms of an arithmetic sequence

ex: 1, 4, 7, 10, . . .

1 2, ,1,

3 3

1. Find the 50th term of 1,4,7, …

2. Find the first term and the common difference of the arithmetic sequence with 8th term 28 and 5th term 10.

3. Find the sum of2 + 5 + 8 + . . . + 41