1. Sum it up
Jeff Bivin -- LZHS

2.
a1 = 1
r = 3
n = 6
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3. –
a1 = 4
r = -2
n = 7
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4. Alternative Sum Formula
We know that:
Multiply by r:
Simplify:
Substitute:
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5. Find the sum of the geometric Series
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6. Find the sum of all the terms in the following GP. 10, 30, 90, ….7290
r = 3, n = ?
an = 7290
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7. Find the sum of all the terms in the following GP. 4, 8, 16, ….2048
r = 2, n = ?
an = 2048
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8. Evaluate = 2 + 4 + 8+…+1024 a1 = 2 r = 2 n = 10 an = 1024
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9. Evaluate = 3 + 6 + 12 +…+ 384 a1 = 3 r = 2 n = 8 an = 384
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10. an = a1·r(n-1) Review -- Geometric Sum of n terms nth term
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11. Geometric
Infinite Series
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12. The Magic Flea (magnified for easier viewing)
There is no flea like a Magic Flea
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13. The Magic Flea (magnified for easier viewing)
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14. Sum it up -- Infinity
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15. Remember --The Magic Flea
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16. Jeff Bivin -- LZHS

17. rebounds ½ of the distance from which it fell --
A Bouncing Ball
rebounds ½ of the distance from which it fell --
What is the total vertical distance that the ball traveled before coming to rest if it fell from the top of a 128 feet tall building?
128 ft
64 ft
32 ft
16 ft
8 ft
Jeff Bivin -- LZHS

18. A Bouncing Ball 128 ft 64 ft 32 ft 16 ft 8 ft Downward
= …
128 ft
64 ft
32 ft
16 ft
8 ft
Jeff Bivin -- LZHS

19. A Bouncing Ball 128 ft 64 ft 32 ft 16 ft 8 ft Upward
= …
128 ft
64 ft
32 ft
16 ft
8 ft
Jeff Bivin -- LZHS

20. A Bouncing Ball 128 ft 64 ft 32 ft 16 ft 8 ft
Downward = … = 256
Upward = … = 128
TOTAL = 384 ft.
128 ft
64 ft
32 ft
16 ft
8 ft
Jeff Bivin -- LZHS

21. rebounds 3/5 of the distance from which it fell --
A Bouncing Ball
rebounds 3/5 of the distance from which it fell --
What is the total vertical distance that the ball traveled before coming to rest if it fell from the top of a 625 feet tall building?
625 ft
375 ft
225 ft
135 ft
81 ft
Jeff Bivin -- LZHS

22. A Bouncing Ball 625 ft 375 ft 225 ft 135 ft 81 ft Downward
= …
625 ft
375 ft
225 ft
135 ft
81 ft
Jeff Bivin -- LZHS

23. A Bouncing Ball 625 ft 375 ft 225 ft 135 ft 81 ft Upward
= …
625 ft
375 ft
225 ft
135 ft
81 ft
Jeff Bivin -- LZHS

24. A Bouncing Ball 625 ft 375 ft 225 ft 135 ft 81 ft
Downward = … =
Upward = … = 937.5
TOTAL = 2500 ft.
625 ft
375 ft
225 ft
135 ft
81 ft
Jeff Bivin -- LZHS

25. Find the sum of the series
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26. Fractions - Decimals
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27. Let’s try again + +
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28. One more
subtract
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29. OK now a series
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30. .9 = 1
.9 = 1
That’s All Folks
Jeff Bivin -- LZHS