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KATRIN_1 [288]
2 years ago
11

Pls help me solve this.

Mathematics
1 answer:
daser333 [38]2 years ago
8 0
The answer is 14 hope this helps
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The geometric sequence a i a i ​ a, start subscript, i, end subscript is defined by the formula: a 1 = 8 a 1 ​ =8a, start subscr
frozen [14]

Question:

The geometric sequence ai is defined by the formula: a₁ = 8, aᵢ = aᵢ₋₁(-1.5 ).

Find the sum of the first 20 terms in the sequence. Choose 1 answer:

Answer:

The sun of 20 terms of the progress is -10,637.621536256

Step-by-step explanation:

Given

Geometric Sequence

a₁ = 8

aᵢ = aᵢ₋₁(-1.5 )

First, the common ratio needs to be calculated.

The common ratio is the ratio of a term to its previous term.

In other words,

Ratio = 2nd term ÷ 1st term or 3rd term ÷ 2nd term, ...... Etc.

We can calculate the common ratio from aᵢ = aᵢ₋₁(-1.5 ) by dividing both sides by aᵢ₋₁. This gives

aᵢ / aᵢ₋₁ = aᵢ₋₁(-1.5 ) / aᵢ₋₁

aᵢ / aᵢ₋₁ = -1.5

So, the common ratio, r = -1.5

Now that we've had the common ratio and first term to be -1.5 and 8 respectively, the sum of 20 terms can then be calculated using the sum of n terms formula.

Sₙ = a(1 - rⁿ)/(1 - r)

We're making use of this formula because r is less than 1

Where n = 20

a = first term = 8

r = -1.5

By substituting these values; we get

S₂₀ = 8(1 - (-1.5)²⁰)/(1 - (-1.5))

S₂₀ = 8(1 - (-1.5)²⁰)/(1 + 1.5))

S₂₀ = 8(1 - (-1.5)²⁰)/(1 + 1.5))

S₂₀ = 8(1 - (3325.25673008

))/(2.5)

S₂₀ = 8(1 - 3325.25673008

)/(2.5)

S₂₀ = 8(-3324.25673008

)/(2.5)

S₂₀ = -10,637.621536256

5 0
3 years ago
Write in lowest terms:<br> 9/(15x)
liq [111]

Answer:

Step-by-step explanation:

3x - 25

 ———————

    5  

Should be something similar to that, sorry If i couldn't help much.

6 0
3 years ago
Bob and ling are playing a number pattern game. Bob wrote the following sequence
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The unknown term is 22.6

28.9
26.8
24.7
22.6
20.5

As you can see, the numbers after the decimal point descends by 1 point. 9 , 8 , 7 , 6 , 5
While the numbers before the decimal point descends by 2 points, 28 , 26 , 24 , 22 , 20


6 0
3 years ago
Read 2 more answers
When this 3-digit number is rounded to the nearest hundred, it rounds to 200.  Rounded to the nearest ten, this number rounds to
alisha [4.7K]
199, it rounds to 200 because it's closer to 200 than 100. It is also closer to 200 than to 190. And finally, 1 + 9 + 9 = 19
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A bike was recently marked down $200.00 from its initial price. if you have a coupon for an additional 30% off after the markdow
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Should be 525$ if I'm correct
5 0
3 years ago
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