2412 Pre-Calculus

Chapter 12 Section 2

ArithmeticSequences

Arithmetic Sequence

A sequence where the elements can be found by

adding the same number to previous terms

2, 5, 8, 11, ___, ___

The number that is added is called the difference d.

d = 314 17325

358

3811

Example 1:

Tell if each sequence is arithmetic and find d if

possible.4, 7, 10, 13, 16 . . .

1/3 ,2/3 , 4/3 , 8/3 . . .

1 , 4 , 9 , 16 , 25 . .

Yes d = 3

No

No

Example 2:

Write the first 4 terms and tell if you have an arithmetic sequence

un = (2n)n

un = 1 + 12(n-1)

un = 5 – 2n

2, 8, 24, 64 No

1, 13, 25, 37 Yes d = 12 3, 1, -1, -3 Yes d= -2

Example 3:

Write the first 5 terms of the arithmetic sequence

u1 = 8, d = 4

u1 = 3, d = -5

u1 = 34, d = 1/2

8,12, 16, 20, 24

3, -2, -7, -12, -17

34, 34.5, 35, 35.5, 36

Finding any Arithmetic term

To find the nth term you can use the formula:

dnaan )1(1

Example 4:

Find the 25th term of: 2, 6, 10, . . .a1 =

d =

n =

2425

)4)(125(225 a

9825 a

Example 5:

Find the 120th term if

a1 = 625

d = -2

n = 120

)2)(1120(625120 a

387120 a

Adding Arithmetic Sequences

To find the sum of n terms you can use the formula:

)( 12 nn

n aaS

Example 5:

Find the sum of the first 50 terms ifa1 = 245

d = 7

n =

an =

50 20825

)588245(

)(

250

50

12

S

aaS nn

n

588

)7)(150(24550

a

A school auditorium is built with seats in rows A through X so that the first row contains 27

seats, the fifth row contains 33 seats.

How many seats are in row B?

How many seats are in row X?

How many seats are in the Auditorium?

Would a school build an auditorium with this many seats?

28 – you can’t have a fractional seat

61 – you can’t have a fractional seat

1056

No – not a good break point for fees