2. Aim: What are the arithmetic series and geometric series? Do Now: Find the sum of each of the following sequences: a) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 b) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 +... + 98 + 99 + 100 HW: p.265 # 12,14,20 p.272 # 6,8,10,16 p.278 # 8,10

3. 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.

4. 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. a 1 = 5; d = 16 – 5 = 11. a 150 = a 1 + d(150 – 1), a 150 = 5 + 11(149) = 1644

5. 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 a 1 = 1 and d = 3 To find the sum, we need to find a 15

6. The sum of an geometric sequence is called geometric series 3, 15, 75, 375, 1875, 9375, 46875, 234375, 1171875 is a geometric sequence, find the sum of sequence. The formula to find the finite (limited number of terms) geometric sequence is

7. Write as a series and then find the sum

8. Infinite series : The last term of the series is the infinity An infinite arithmetic series has no limit An infinite geometric series has no limit when An infinite geometric series has a finite limit when the limit can be found by the formula

9. Find the sum of the following infinite geometric sequence: 4, 4(0.6), 4(0.6) 2, 4(0.6) 3,..., 4(0.6) n - 1,... a 1 = 4 and r = 0.6 Find

10. Find the sum of the first 10 terms of the geometric series Find the sum of five terms of the geometric series whose first term is 2 and fifth term is 162 S 5 = 242