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nikdorinn [45]
2 years ago
11

12) Find the sum, S7, for the geometric series (1 + 5 + 25+ --- + 15625).

Mathematics
1 answer:
vfiekz [6]2 years ago
8 0

Answer:

Find the (r) between adjacent members

a2/a1=+25/5=5

a3/a2=+125/+25=5

a4/a3=+625/+125=5

a5/a4=+3125/+625=5

a6/a5=+15625/+3125=5

The ration (r) between every two adjacent members of the series is constant and equal to 5

General Form: a

n

=a

1

×r

n-1

This geometric series: a

n

=5×5

n-1

The nature of this series

Sum of finite geometric series members

sum of a geometric series

The sum of our particular series

a 1-rn = 5 1-56 = 5 1-15625 = 5 -15624 =5×3906=19530

1-r 1-5 -4 -4

Finding the n

th

element

a2 =a1×r2-1  =a1×r1 =5×51 =25

a3 =a1×r3-1  =a1×r2 =5×52 =125

a4 =a1×r4-1  =a1×r3 =5×53 =625

a5 =a1×r5-1  =a1×r4 =5×54 =3125

a6 =a1×r6-1  =a1×r5 =5×55 =15625

a7 =a1×r7-1  =a1×r6 =5×56 =78125

a8 =a1×r8-1  =a1×r7 =5×57 =390625

a9 =a1×r9-1  =a1×r8 =5×58 =1953125

a10 =a1×r10-1  =a1×r9 =5×59 =9765625

a11 =a1×r11-1  =a1×r10 =5×510 =48828125

a12 =a1×r12-1  =a1×r11 =5×511 =244140625

a13 =a1×r13-1  =a1×r12 =5×512 =1220703125

a14 =a1×r14-1  =a1×r13 =5×513 =6103515625

a15 =a1×r15-1  =a1×r14 =5×514 =30517578125

a16 =a1×r16-1  =a1×r15 =5×515 =152587890625

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Step-by-step explanation:

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Pyramid A has a triangular base where each side measures 4 units and a volume of 36 cubic units. Pyramid B has the same height,
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Answer:

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Step-by-step explanation:

Given

<u>Pyramid A</u>

s = 4 -- base sides

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<u>Pyramid B</u>

s = 6 --- base sides

Required

Determine the volume of pyramid B <em>[Missing from the question]</em>

From the question, we understand that both pyramids are equilateral triangular pyramids.

The volume is calculated as:

V = \frac{1}{3} * B * h

Where B represents the area of the base equilateral triangle, and it is calculated as:

B = \frac{1}{2} * s^2 * sin(60)

Where s represents the side lengths

First, we calculate the height of pyramid A

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B = \frac{1}{2} * s^2 * sin(60)

B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}

B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}

B = 4\sqrt 3

The height is calculated from:

V = \frac{1}{3} * B * h

This gives:

36 = \frac{1}{3} * 4\sqrt 3 * h

Make h the subject

h = \frac{3 * 36}{4\sqrt 3}

h = \frac{3 * 9}{\sqrt 3}

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To calculate the volume of pyramid B, we make use of:

V = \frac{1}{3} * B * h

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The base area B, is then calculated as:

B = \frac{1}{2} * s^2 * sin(60)

Where

s = 6

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B = \frac{1}{2} * 6^2 * sin(60)

B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}

B = 9\sqrt 3

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V = \frac{1}{3} * B * h

Where

B = 9\sqrt 3 and h = \frac{27}{\sqrt 3}

V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}

V = \frac{1}{3} * 9 * 27

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Answer:

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Step-by-step explanation:

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Divide the numbers from left to right.

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First, subtract by 70 from both sides.

70-t-70=30-70

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30-70=-40

<u>Rewrite the problem down.</u>

-t=-40

Divide by -1 from both sides.

-t/-1=-40/-1

<u>Solve.</u>

<u />

<u>Divide the numbers from left to right.</u>

-40/-1=40

<h3><u>t=40</u></h3>

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I hope this helps! Let me know if you have any questions.

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2 years ago
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