Lesson 11.4 Alg-1 Write the recursive formula for each sequence 1, 11, 21, 31, … 𝑎 𝑛 =−4+ 𝑛−1 6 4 1 2 , 2, − 1 2 , −3, … 𝑎 𝑛 =3+ 𝑛−1 (−1) 4 Alg-1 5 Alg-1 Calculate the indicated term Calculate the indicated term 𝑎 5 =−4 𝑎 21 =23 𝑎 5 =−4 𝑎 𝑛 = 𝑎 𝑛−1 +4 𝑎 𝑛 = 𝑎 𝑛−1 −1.2 𝑎 6 = 𝑎 22 = 𝑎 𝑛 = 𝑎 𝑛−1 +4 𝑎 10 = Lesson 11.4 Alg-1

Homework Corrections Lesson 11.3 Worksheet all

Calendar 11.4 Unit 2 Test 2 Review Unit 2 Test 2 12.1a 12.1b 12.1c Monday Tuesday Wednesday Thursday Friday 11.4 Unit 2 Test 2 Review Unit 2 Test 2 12.1a 12.1b 12.1c 12.2a 12.2b 12.3a 12.3b Quiz, 12.4 13.1 13.2 13.3 No School

Homework Lesson 11.4 Worksheet all Class Rules!!! No getting up without asking 2. No talking until activities 3. Take Notes! DO ALL EXAMPLES Raise your hand

Recursive Formula for Arithmetic Sequences Lesson 11.4

Objective Given an arithmetic sequence I can write its recursive formula I can convert from explicit to recursive formula I can calculate the next term given a recursive formula

Last Few Classes… 5, 10, 15, 20, … 𝑎 𝑛 = 𝑎 1 + 𝑛−1 𝑑 𝑎 3 = 15 𝑓(3)=15 Arithmetic Sequences 5, 10, 15, 20, … 𝑎 𝑛 = 𝑎 1 + 𝑛−1 𝑑 Explicit 𝑎 3 = 15 𝑓(3)=15

Something new today…

Some background…

Here’s the idea… 5, 10, 15, 20, … 𝑎 𝑛−1 𝑎 𝑛 𝑎 2 𝑎 3

Today’s Task… 5, 10, 15, 20, … 𝑎 𝑛

Recursive Formula 𝑎 𝑛 = 𝑎 𝑛−1 +𝑑 Previous term Common Difference

Today’s Tasks Write the recursive formula for a given sequence Convert recursive to explicit formula Given a term of a sequence and the common difference, find the next term(s)

Today’s Tasks Write the recursive formula for a given sequence

Example 𝑎 𝑛 = 𝑎 𝑛−1 +𝑑 𝑎 𝑛 = 𝑎 𝑛−1 +𝑑 𝑎 𝑛 = 𝑎 𝑛−1 +5 𝑎 𝑛 = 𝑎 𝑛−1 −7 5, 10, 15, 20, … -3, -10, -17, -24, … 𝑎 𝑛 = 𝑎 𝑛−1 +𝑑 𝑎 𝑛 = 𝑎 𝑛−1 +𝑑 𝑎 𝑛 = 𝑎 𝑛−1 +5 𝑎 𝑛 = 𝑎 𝑛−1 −7

Write the recursive formula for each sequence 1, 11, 21, 31, … 4 1 2 , 2, − 1 2 , −3, … 𝑎 𝑛 = 𝑎 𝑛−1 +𝑑 𝑎 𝑛 = 𝑎 𝑛−1 +𝑑 𝑎 𝑛 = 𝑎 𝑛−1 +10 𝑎 𝑛 = 𝑎 𝑛−1 −2 1 2

Review Given an arithmetic sequence I can write its recursive formula I can convert from explicit to recursive formula I can calculate the next term given a recursive formula

What if you had the explicit formula? 𝑎 𝑛 =−3+ 𝑛−1 2 𝑎 𝑛 = 𝑎 𝑛−1 +𝑑 𝑎 𝑛 = 𝑎 𝑛−1 +2

What if you had the explicit formula? 𝑎 𝑛 =1.6+ 𝑛−1 (−75) 𝑎 𝑛 = 𝑎 𝑛−1 +𝑑 𝑎 𝑛 = 𝑎 𝑛−1 −75

Write the recursive formula for each sequence 𝑎 𝑛 =−4+ 𝑛−1 6 𝑎 𝑛 =3+ 𝑛−1 (−1) 𝑎 𝑛 = 𝑎 𝑛−1 +𝑑 𝑎 𝑛 = 𝑎 𝑛−1 +𝑑 𝑎 𝑛 = 𝑎 𝑛−1 +6 𝑎 𝑛 = 𝑎 𝑛−1 −1

Review Given an arithmetic sequence I can write its recursive formula I can convert from explicit to recursive formula I can calculate the next term given a recursive formula

Using the recursive formula 𝑎 41 =10 𝑎 𝑛 = 𝑎 𝑛−1 +3 𝑎 42 = 13 𝑎 42 = 𝑎 42−1 +3 𝑎 42 = 𝑎 41 +3 𝑎 42 =10+3

Using the recursive formula 𝑎 7 =−4 𝑎 𝑛 = 𝑎 𝑛−1 −2 𝑎 8 = −6 𝑎 8 = 𝑎 8−1 −2 𝑎 8 = 𝑎 7 −2 𝑎 8 =−4−2

Calculate the indicated term 𝑎 5 =−4 𝑎 21 =23 𝑎 𝑛 = 𝑎 𝑛−1 +4 𝑎 𝑛 = 𝑎 𝑛−1 −1.2 𝑎 6 = 𝑎 22 = 21.8 𝑎 6 = 𝑎 6−1 +4 𝑎 22 = 𝑎 22−1 −1.2 𝑎 6 = 𝑎 5 +4 𝑎 22 = 𝑎 21 −1.2 𝑎 6 =−4+4 𝑎 22 =23−1.2

Think about this…

Using the recursive formula 𝑎 7 =−4 𝑎 8 −6 𝑎 𝑛 = 𝑎 𝑛−1 −2 𝑎 9 −8 𝑎 11 = 𝑎 10 −10 𝑎 8 = 𝑎 8−1 −2 𝑎 11 −12 𝑎 8 = 𝑎 7 −2 𝑎 8 =−4−2

Calculate the indicated term 𝑎 5 =−4 𝑎 6 =0 𝑎 𝑛 = 𝑎 𝑛−1 +4 𝑎 7 =4 𝑎 10 = 𝑎 8 =8 𝑎 9 =12 𝑎 6 = 𝑎 6−1 +4 𝑎 10 =16 𝑎 6 = 𝑎 5 +4 𝑎 6 =−4+4

Review Given an arithmetic sequence I can write its recursive formula I can convert from explicit to recursive formula I can calculate the next term given a recursive formula

Lesson 11.4 Worksheet all Homework End of Class Rules!!! 1. Clean Up your Area Wait in your chairs 3. I dismiss not the bell 4. Push in your chairs 5. Keep it to a low roar