Do Now You have 5 minutes to complete

Do Now : You have 5 minutes to complete the problems below. 1. Determine whether each sequence is arithmetic. Identify the common difference. • -26, -33, -40, … • 0. 6, 0. 9, 1. 2, 1. 8, … 2. Find the 20 th term of the arithmetic sequence for which a 1 = 56 and d = -5

Focus Question: How can we find the sum of an Arithmetic series? FEBRUARY 5, 2014

Daily Professionalism Grade TAKE 2 MINUTES TO DISCUSS W/I YOUR GROUPS A PROFESSIONALISM TRAIT THAT YOU SHOULD DISPLAY DAILY.

Arithmetic Series (don’t copy) The African-American celebration of Kwanzaa involves the lighting of candles every night for seven nights. The first night one candle is lit and blown out. The second night a new candle and the candle from the first night are lit and blown out. The third night a new candle and the two candles from the second night are lit and blown out. This process continues for the seven nights. We want to know the total number of lightings during the seven nights of celebration.

Arithmetic Series (don’t copy) The first night one candle was lit, the 2 nd night two candles were lit, the 3 rd night 3 candles were lit, etc. So to find the total number of lightings we would add: 1 + 2 + 3 + 4 + 5 + 6 + 7= 28

Sum of Arithmetic Series Divide n by 2 and multiply it by the sum of the first and last term.

Lets Try: Find the sum of the first 100 terms of the arithmetic series with a 1 = 1 and a 100 =100 S 100 = 100/2(1 + 100) = 50(101) = 5050

You Try – Example 2 Find the sum of the first 10 terms of the arithmetic series with a 1 = 6 and a 10 =51 S 10 = 10/2(6 + 51) = 5(57) = 285

Example 3 Find the sum of the first 50 terms of an arithmetic series with a 1 = 28 and d = -4 We need to know n, a 1, and a 50. n= 50, a 1 = 28, a 50 = ? ? We have to find it a 50

Examples a 50 = 28 + -4(49) = -168 So n = 50, a 1 = 28, & an =-168 S 50 = (50/2)(28 + -168) = 25(-140) = -3500

Definition Arithmetic Means: the terms between any two nonconsecutive terms of an arithmetic sequence.

Arithmetic Means Find three arithmetic means between 8 and 14.

Arithmetic Means So our sequence must look like 8, __, __, 14. In order to find the means we need to know the common difference. We can use our formula to find it.

Arithmetic Means 8, __, __, 14 a 1 = 8, a 5 = 14, & n = 5 14 = 8 + d(5 - 1) 14 = 8 + d(4) 8 6 = 4 d 1. 5 = d subtract divide by 4

Arithmetic Means 8, __, __, 14 so to find our means we just add 1. 5 starting with 8. 8, 9. 5, 11, 12. 5, 14

YOU TRY Find 4 arithmetic means between 10 and 45 10, __, __, 45 a 1 = 10, a 6 = 14, & n = 6 45 = 10 + d(6 - 1) 45 = 10 + d(5) 35 = 5 d 7 = d subtract 10 divide by 5