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gizmo_the_mogwai [7]
3 years ago
11

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

ipt, 1, end subscript, equals, 8 a i = a i − 1 ⋅ ( − 1.5 ) a i ​ =a i−1 ​ ⋅(−1.5)a, start subscript, i, end subscript, equals, a, start subscript, i, minus, 1, end subscript, dot, left parenthesis, minus, 1, point, 5, right parenthesis Find the sum of the first 20 2020 terms in the sequence. Choose 1 answer:
Mathematics
1 answer:
frozen [14]3 years ago
5 0

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

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On a map, the equal sign in 1 in. = 30 mi does not mean that the two quantities are equal, as it would in an equation.

A scale is the ratio that compares a length in a drawing to the corresponding length in the actual object. If a 30-mile road is 1 in. long on a map, you can write the scale of the map in these three ways:

Go here for more. http://www.phschool.com/itext/mgmath_course2/Ch05/05-07/PH_MSM2_ch05-07_Obj1.html
4 0
3 years ago
i used the answer key to get my answer and checked it with my dumb useless teacher and it’s right but, he won’t tell me how to g
gizmo_the_mogwai [7]
You multiply it with the same number you use for the denominator.
in this case 3/4 and 7/10
you find the LCM of the denominator is 20
so for 4 to become 20 you multiply by 5 then for the numerator 3 also multiply by 5, so you get 15/20
its the same also with 7/10, you multiply both the numerator and the denominator by 2 and get 14/20
hope it help... :)




7 0
3 years ago
There are 18 bikes in a bike rack. There are 4 more blue bikes than yellow bikes,and 2 less yellow bikes than green bikes.how ma
Phoenix [80]
Y+4= x blue bikes
G-2= x yellow bikes

4y+4= 8 blue bikes
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4y= 4 yellow bikes

8 blue bikes
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5 0
3 years ago
Please help with the following problem asap!!
umka21 [38]

Answer:

8^7

Step-by-step explanation:

\dfrac{8^{15}}{8^7 \cdot 8} =

Remember that 8 = 8^1.

= \dfrac{8^{15}}{8^7 \cdot 8^1}

When you multiply powers with the same base, add the exponents. Do this in the denominator.

= \dfrac{8^{15}}{8^{7+1}}

= \dfrac{8^{15}}{8^{8}}

When  you divide powers with the same base, subtract the exponents.

= 8^{15-8}

= 8^7

4 0
3 years ago
Find the area of △LKJ.
nirvana33 [79]

Answer:

A=600\: u^{2}

<u>The correct answer is letter c.</u>

Step-by-step explanation:

The area equation of a triangle is given by:

A=\frac{bh}{2}  (1)

Where:

b is the base

h is the height

Let's find first the angle MJK (α), using the tangent definition.

tan(\alpha)=\frac{24}{32}

\alpha=tan^{-1}(\frac{24}{32})

\alpha=36.9^{\circ}

Now, if α = 37° then β (angle JLK) must be:

37^{\circ} + \beta + 90^{\circ}=180^{\circ}

\beta=53^{\circ}

Now, we can find the distance ML using again the tangent definition:

tan(\beta)=\frac{24}{ML}

ML=\frac{24}{tan(53)}

ML=18

The base of the triangle LKJ will be:

b=32+ML=32+18=50

Therefore, using equation (1) the area of △LKJ will be:

A=\frac{50*24}{2}

A=600\: u^{2}

The correct answer is c.

I hope it helps you!

5 0
3 years ago
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