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Mice21 [21]
3 years ago
8

What is the sum of the first five terms of a geometric series with a1=15 and r=1/3

Mathematics
2 answers:
Solnce55 [7]3 years ago
6 0

Answer:

15, 5, 5/3, 5/9, 5/27

Step-by-step explanation:

Recall, that the general form of a geometric series is

a, ar, ar², ar³, .........

where a is the first term and r is the ratio

It is given that the first time is 15, hence a = 15

also given that ratio is 1/3

hence the first 5 terms are:

15, (15)(1/3), (15)(1/3)^2, (15)(1/3)^3, (15)(1/3)^4

simplifying each term gives

15, 5, 5/3, 5/9, 5/27

Talja [164]3 years ago
3 0

Answer:

605/27 or 22.41 to the nearest hundredth.

Step-by-step explanation:

The formula for the sum of n terms is

an = a1 *  (1 - r^n) / (1 - r)  where a1 = the first term and r = the common difference.

So here a5 =  15 * (1 - (1/3)^5) / (1 - 1/3)

= 605/27

= 22.41 to the nearest hundredth.

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3 years ago
Dilate by a scale<br> factor of 1/2<br> AL<br> D
Firdavs [7]

Answer:

The image triangle ΔD'L'W' after the dilation by a scale factor of 1/2 will have the vertices:

  • D' (0, 1)
  • L' (1/2, 5/2) or L'(0.5, 2.5)
  • W' (5/2, 2) or W'(2.5, 2)

`The figure of the dilated image is attached below.

Step-by-step explanation:

Given the triangle ΔDLW withe the vertices

  • D(0, 2)
  • L(1, 5)
  • W(5, 4)

As the scale factor 1/2 < 0, thus the image triangle will be smaller than the original triangle.

The rule of dilation is given by

Dilation: (x, y)  →  (1/2x, 1/2y), centered at (0, 0)

D(0, 2)  → D' (1/2x, 1/2y) → D' (1/2(0), 1/2(2)) = D' (0, 1)

L(1, 5)  → L'(1/2x, 1/2y) →  L'(1/2(1), 1/2(5)) = L' (1/2, 5/2)

W(5, 4)  → W'(1/2x, 1/2y) →  W'(1/2(5), 1/2(4)) = W' (5/2, 2)

Therefore, the image triangle ΔD'L'W' after the dilation by a scale factor of 1/2 will have the vertices:

  • D' (0, 1)
  • L' (1/2, 5/2) or L'(0.5, 2.5)
  • W' (5/2, 2) or W'(2.5, 2)

`The figure of the dilated image is attached below.

7 0
3 years ago
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krok68 [10]

Answer:

1. 5/6

2. 7/8

3. 1/2

4. 5/4

5. 4/5

6. 5/4

7. 11/12

8. 5/2

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10. 2/3

11. 13/20

12. 1/12

13. 7/22

14. 7/18

15. 2/3

16. 5/12

17. 5/12

18. 3/8

4 0
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