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Means for Series Find the value(s) missing from a list.

Means for Series Find the value(s) missing from a list. Flashback to Arithmetic. 6, ___,14… 6+14 =20 20/2=10 6,10,14 counting by 4 when you start at 6. Arithmetic Series. Find the missing means. 8,____, 18 2) 12, _____, 38 3) 20,___,____,____,36. Check this out.

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Means for Series Find the value(s) missing from a list.

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  1. Means for SeriesFind the value(s) missing from a list.

  2. Flashback to Arithmetic • 6, ___,14… • 6+14 =20 • 20/2=10 • 6,10,14 counting by 4 when you start at 6

  3. Arithmetic Series • Find the missing means. • 8,____, 18 2) 12, _____, 38 3) 20,___,____,____,36

  4. Check this out • Use the series: 5, 10, 20 • Take the first and third terms. • Multiply • Then square root. • = 10 the geometric mean between 5 and 20. • List the next two terms: 5, 10, 20, 40, 80 • Take 5 & 80, multiply then root to find the mean. • Then try 20 and 80.

  5. Formula for d.(last known value-first known value)/number of terms

  6. Find the missing terms of each geometric sequence • 1) 3, ____, 12 • 2) 45, ___, 180 • 3) 60, ___, (20/3) • 4) 9180, _____, 255 • 5) -20, ___, ___, ____, -1.25

  7. Let’s see something • Is 3+5 =5+3? • So 3+10+17+24+31+38= • 38+ 31+24+17+10+ 3? • first value + last value = 3+38=41 6*41 = 246 246/2= 123 Now we have the formula for the sum of an arithmetic sequence.

  8. Formula for a partial sum

  9. Try • Find the sum of the first 50 positive integers. • Find the sum: 7, 14, 21….98 • Find the sum: 10, 4, (-2), (-8)….(-50)

  10. Distributive Law • 10+5x= 5(_______________) • 5+5x = 5(____________) • -r =(____________)

  11. Clever Time • Take a geometric sequence Multiply by -r. Shift the list over one space and add. = 5 15 45 135 405 -r = -15 -45 -135 -405 -1215 -r = 5 -1215

  12. Sum of a Finite Geometric Series With r not equal to 1!

  13. Try • Geometric Series problems 1-5

  14. The sum of an infinite geometric series • If <1 = • If • Show a number line.

  15. Fibonacci Sequence

  16. A different pattern • Use two started values. • Start making the list using the formula

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