ARITHMETIC SEQUENCES AND SERIES

Arithmetic sequence The terms of the sequence have a common difference between them This means that when you subtract consecutive terms, you always get the same number

Example Determine if each sequence is arithmetic. If yes, find the common difference 1, 4, 7, 10, 13, 16 15, 10, 5, 0, -5, -10 1, ½ , 0, - ½ , -1, - 3/2 1, 4, 9, 16, 25, 36, 49 Yes, d = 3 Yes, d = -5 Yes, d = - ½ no

Finding the formula for an arithmetic sequence an = dn + c We did this yesterday sometimes when we found the pattern of a sequence Find the common difference. This will be the number multiplied by n Find the 0th term. This will be the number added (it is called “c” in the formula)

Example Write a formula for the arithmetic sequence and find the 100th term (a100) 1, 4, 7, 10... 15, 10, 5, 0, … 1, ½ , 0, - ½ ,...... d = 3, a0 = -2 an = 3n - 2 a100 = 298 a100 = -480 d =-5, a0 = 20 an = -5n + 20 d =- ½ , a0 = 3/ 2 an = - ½ n + 3/2 a100 = -48.5

Example Find the 102nd term of an arithmetic sequence with a common difference of 2 if the first term is 7 a102 = 205 d = 2, a0 = 5 an = 2n + 5

Example If a1 = 12, and a2 = 17, find a32 a32 = 167 d = 5, a0 = 7 an = 5n + 7

ARITHMETIC SERIES To find the sum of an arithmetic series, use the formula: First term Last term Number of terms

Example n = 95 (97-3+1), a3 = 5, a97 = 197 You can also use your calculator

Example Find the indicated nth partial sum. 40, 29, 18, 7, …. n = 10 an= -11n+51 a10= -59

EXAMPLE A theater has 60 seats in the first row, 68 seats in the second row, 76 seats in the third row and so on in the same increasing pattern. If the theater has 20 rows of seats, how many seats in the theater an = 8n+52 a20 = 212