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Recursive and Explicit Formulas for Arithmetic Sequences

Learn how to find numbers in arithmetic sequences using recursive and explicit formulas. Understand the concept of common difference and its relationship with slope. Practice solving arithmetic sequence problems.

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Recursive and Explicit Formulas for Arithmetic Sequences

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  1. Week 5 Warm Up 09.12.11 { -3, 8, 19, 30, 41, . . } n = 3 1) tn = 2) tn - 1= 3) t6 =

  2. a = { 4, 7, 10, 13, 16, . . .} Re 1 then a3 - 1= if a3 = 10 7 d = 3 Recursive Formula: Arithmetic an= an - 1+ 3 a50 = a49+ 3

  3. Explicit Formula You Do not need to know the previous number to find a number in the sequence. an = dn + a0 Ex 1

  4. Ex 2 • • • •

  5. Ex 2 • output: 4, 7, 10, 13, • • • input: 1, 2, 3, 4 common difference? goes up by 3 common difference = slope

  6. • • • • • y = mx + b Ex 3 y = x + 3 1 Explicit Formula an = 3n + 1

  7. • • • • • • an = 3n + 1 an = 3n + 1 Ex 4 a3 = 3(3) + 1 a50 = 3(50) + 1 a3 = 9 + 1 a50 = 150 + 1 a3 = 10 a50 = 151

  8. a = { 10, 8, 6, 4, 2,. . .} Ex 5 y = -2x + 12 12 tn = -2n + 12 10 t0 = -2(0) + 12 8 6 t0 = 12 4 t0 = y-intercept

  9. Explicit Formula: Arithmetic Sequence an = dn + a0 -2, 7, 16, 25, . . . Ex 6 d = 9 a0 = -11 an = 9n - 11

  10. Do: 1 What is the explicit formula? -6, 1, 8, 15, 22, . . . Assignment: Handouts – 1.3 Day 1 Explicit Formulas

  11. a10 an = -2n + 12 a10 = -2( 10 ) + 12 a10 = -20 + 12 a10 = -8

  12. • • • • • • an = 3n + 1 Ex 5 a0 = 3(0) + 1 a0 = 0 + 1 a0 is the y-intercept a0 = 1

  13. Re 1 Recursive Formulas You have to know the previous number to find the next number. = tn tn– 1 + d Arithmetic Geometric tn = r ( ) tn-1

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