Aim: What is the arithmetic series ? Do Now: Find the sum of each of the following sequences: a) 1 +...

Aim: What is the arithmetic series ?

Do Now: Find the sum of each of the following sequences:

a) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19b) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + . . . + 98 + 99 + 100

HW: p. 264 # 4,5,7 p.265 # 12,14,16,20,22

The sum of an arithmetic sequence is called arithmetic series

Although we can find the arithmetic series one after the other, there is a formula to find the series faster.

2

)( 1 nn

aanS

5050)101(502

)1001(100100

S

Find the sum of the first 150 terms of the arithmetic sequence 5, 16, 27, 38, 49, . . .

First we need to determine what the last term of the 150 terms (or the 150th term) is.

a1 = 5; d = 16 – 5 = 11.

a150 = a1 + d(150 – 1), a150 = 5 + 11(149) = 1644

123675)1649(752

)16445(150150

S

Write the sum of the first 15 terms of the arithmetic series 1 + 4 + 7 + · · · in sigma notation and then find the sum

First of all, we need to find the recursive formula

),1(31 nan

a1 = 1 and d = 3

23 nan

15

1

23n

n

330)22(152

)44(15

43421)14(3115 aTo find the sum, we need to find a15

2

)431(1515

S

We first need to find the 1st and 35th term

Find the value of the following summation

(48 – 15) + 1 = 34

There are 33 terms between 15th and 47th term