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
How do i solve this for x
Lostsunrise [7]
C) The 2 triangles are similar , then we can write:

5x/45 = 20/36 . Cross multiplication:

5x*36 = 45*20
180x = 900   and x = 900/180 , x = 5 (and 5x = 25)

d) Remember the proportionality theorem (or Thales')
You can write the following proportion:
GH/HJ = KL/LM
8/6 = 10/x . Cross multiplication:

8x = 60 and x = 60/8 , x = 7.5

3 0
3 years ago
Which expression is equivalent to -28 x 2 + 35 x ?
IrinaVladis [17]

Answer:

35+28=31

Step-by-step explanation:

7 0
3 years ago
What is 52% of 25? plzz helppp
Sonbull [250]

Answer: its 13

Step-by- 52 percent *25 =

(52:100)*25 =

(52*25):100 =

1300:100 = 13

step explanation:

5 0
2 years ago
Read 2 more answers
A recipe requires 1/3 cup of water for every 2/5 cups of sugar. How much
Anni [7]

Answer:

1 1/5

Step-by-step explanation:

4 0
2 years ago
The angles shown are complementary angles. The measure of angle 1 is ​(14x-21​) degrees and the measure of angle 2 is ​(​4x+75)
Anni [7]

Answer:

A complementary angle is an angle that adds up to 90 degrees. supplementary angles add up to 180 degrees. So a supplementary angle lies on a single, straight line, and a complementary angle is a right angle.

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • The Mason family drove round trip from their house to their son's college campus in 5 in a half hours. If the distance from the
    14·1 answer
  • Write an equation equal to -(16-9)
    14·1 answer
  • What's 998 X by 8? ( plz answer i hav 2 more )
    9·1 answer
  • Help please. my sister cant figure this out
    6·1 answer
  • If u come across this can you PLEASE HELP
    8·1 answer
  • HELP PLZ !!?
    15·1 answer
  • What equation is part of the same fact family as <br> 8 x 5 = 40
    5·1 answer
  • Solve (x^3-4x)(2x^2-3x)​
    15·1 answer
  • Can Someone Help? Im already failing Math Badly
    7·2 answers
  • If a shirt costs 45 dollars, it's marked down to 30% off, what is the amount of the discount?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!