13.3 Arithmetic & Geometric Series

A series is the sum of the terms of a sequence. A series can be finite or infinite. We often utilize sigma notation to denote a series is the greek letter sigma – stands for “sum” Ex 1) Express 3 – 6 + 9 – 12 + 15 using sigma notation - five terms - alternating signs - rule 3k Ex 2) Find the following sums. a) b) index sequence rule = 140

is an infinite series. The sum of the first n terms is called the nth partial sum of the series and is denoted by Sn. Ex 3) Find the indicated partial sum. a) S10 for –3 – 6 – 9 – 12 – 15 – 18 – 21 – 24 – 27 – 30 = –165 b) S6 for keep going… = 4 + 14 + 24 + 34 + 44 + 54 = 174 Writing out all these terms is cumbersome! We have formulas! If a1, a2, a3, … is an arithmetic sequence with common difference d an = a1 + (n – 1)d Which should you use? Discuss advantages of each! or

Ex 4) Find the indicated partial sum. a) S8 for 15, 9, 3, –3, … use b) S24 for use We can also use a formula for the sum of a geometric series. If a1, a2, a3, … is a geometric sequence with common ratio r an = a1rn–1 = 306 Ex 5) Find the partial sum S7 for the series 1 – 0.8 + 0.64 – 0.512 + … Be careful! Watch order of operations!

Ex 6) Marc’s grandmother gives him $100 on his birthday every year beginning with his third birthday. It is deposited in an account that earns 7.5% interest compounded annually. a1 = 100 r = 1.075 (why the 1??) How much is the account worth the day after Marc’s 10th birthday?