1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
What would the answer be ? Thank You!!
Bogdan [553]

Answer:

2.33 = BC

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan B = AC / BC

tan 25 = AC / 5

Multiply each side by 5

5 tan 25 = BC

2.331538291 = BC

To the nearest hundredth

2.33 = BC

3 0
3 years ago
PLEEEEEEASE HELP MEEEEE!! ill give you 20 points
Nana76 [90]
331.3%
Convert 53/16 to simplest form, 3 5/16, convert 5/16 into numbers —> 0.3125
Take the whole number and add it into the ones place: 3.3125
Move the decimal into two places then round to the nearest tenth: 331.3
8 0
3 years ago
If 5-3(2a+1)=-4a+10, what is the value of a+2​
AlekseyPX

Answer:

-2

<em>BRAINLIEST, PLEASE!</em>

Step-by-step explanation:

5 - 3(2a + 1) = -4a + 10

5 - 6a - 3 = -4a + 10

2 - 6a = -4a + 10

-2a = 8

a = -4

-4 + 2 = -2

5 0
3 years ago
Read 2 more answers
B 95 C a e 75° 709 ITEM BANK: Move to Bottom 25° 30° 35° 50° 75° 85°​
den301095 [7]

Answer:

85 California spout alone 1

3 0
3 years ago
(Repost) please help what is 7 7/10 rounded to the nereast whole number?? please explain your answer if you got it cause I can L
Finger [1]
It’s eight because 7 can round up so it changed to eight
7 0
3 years ago
Read 2 more answers
Other questions:
  • Barrett purchased a piece of sandpaper for his electric sander, as shown above. The radius of the sandpaper is 2.5 inches.
    14·2 answers
  • Which graph is a histogram
    15·1 answer
  • While taking inventory at her bakery, Ruby noticed that she had 5⁄6 pound of cinnamon yesterday, but now had only 2⁄3 pound. How
    11·2 answers
  • Students in a cooking class made 4 1/2 quarts of soup. They served 4/5 of the soup to friends. Each serving is 3/5 quart. Hector
    7·1 answer
  • Write <br> 45<br> as a product of prime factors.
    12·1 answer
  • II. The results of a recent survey indicate that the average new car costs $23,000, with a standard deviation of $3,500. The pri
    8·1 answer
  • you and your friend start biking to opposite directions from the same point. You travel 108 feet every 8 seconds. Your friend tr
    10·1 answer
  • The selling price of an item is ​$650. It is marked down by ​%10, but this sale price is still marked up from the cost of ​$450.
    5·2 answers
  • 5) Write the missing numbers to find the<br> quotient of 782 = 17. So that 782 = 17 = 46
    5·1 answer
  • Find the slope of the line passing through the points (4, 4) and (4, - 4) .
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!