Pre Calculus 11 Section 1.2 Arithmetic Series

Jan ’14 Feb ’14 Mar ’14 Apr ’14 May ’14 Jun ’14 Ever wonder how much would be in your bank account after 2 years if you deposited $100 in the 1st month and increased each monthly deposit by $30? Jan ’14 Feb ’14 Mar ’14 Apr ’14 May ’14 Jun ’14 $100 $130 $160 $190 $220 $250 In the 1st 6 months of ‘07, your bank account would have: 100 + 130 + 160 + 190 + 220 + 250 = 1050 Over 2 years you would have to add 24 numbers up. UGH! For any arithmetic sequence, there will be a high and low and these 2 numbers will always average out.

Jan ’14 Feb ’14 Mar ’14 Apr ’14 May ’14 Jun ’14 $100 $130 $160 $190 $220 $250 $350 If you add the 1st and last numbers or any other pair you get the same answer. (100 + 250)=350, 130 + 220=350, 160 + 190 = 350 Every two terms make a pair, so with 6 terms there are 3 pairs (100 + 250)x 3= 1050 Sum of any arithmetic sequence:

Formula for the Sum of an Arithmetic Sequence: The sum of an arithmetic series up to the “nth” term is denoted “Sn” If we group the first with the last term and also every term in between, we will have n/2 number of equal pairs If we group the first and last term, the value will be equal to 2a+(n–1)d The sum will then be the value of each pair times the number of pairs © Copyright all rights reserved to Homework depot: www.BCMath.ca

Ex. 1: Find the sum of the 1st 36 terms of the arithmetic sequence -8, -3, 2, 7, . . . Determine parts you know: a = -8, n = 36, tn = ?, Sn = ? We need to know tn to find Sn. Use prior knowledge. Recognize this? = -8 + (36 – 1) 5 = 167 Sub parts into formula and solve.

Ex: Find the sum up to the 10th term: Use the General Term Formula to find the last term Ex: Find the sum up to the 100th term: © Copyright all rights reserved to Homework depot: www.BCMath.ca

Solve for Sn. Ex. 2: Find the sum of 53, 49, 45, . . . , -51 Determine known parts. a = 53, tn = -51, n = ?, Sn = ? Find “n” using prior knowledge. Solve for Sn.

Ex: Find the Sum of the arithmetic series: Find out how many terms there are by using the General Term formula: Find the Sum with the Formula: Since it’s an arithmetic series, then (t3 – t2 )= (t4 – t3 ) = d © Copyright all rights reserved to Homework depot: www.BCMath.ca

Hw: Assignment 1.2 Arithmetic Series Optional pg 27 #1 – 6 Odd letters, 7 - 15 Odd