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
Gelneren [198K]
3 years ago
8

The question is in the image below.

Mathematics
1 answer:
sineoko [7]3 years ago
3 0

Answer:

The Recursive Formula for the sequence is:

\:a_n=\frac{1}{5}\left(a_{n-1}\right)     ; a₁ = 125

Hence, option D is correct.

Step-by-step explanation:

We know that a geometric sequence has a constant ratio 'r'.

The formula for the nth term of the geometric sequence is

a_n=a_1\cdot r^{n-1}

where

aₙ is the nth term of the sequence

a₁ is the first term of the sequence

r is the common ratio

We are given the explicit formula for the geometric sequence such as:

a_n=125\left(\frac{1}{5}\right)^{n-1}

comparing with the nth term of the sequence, we get

a₁ = 125

r = 1/5

Recursive Formula:

We already know that

  • a₁ = 125
  • r = 1/5

We know that each successive term in the geometric sequence is 'r' times the previous term where 'r' is the common ratio.

i.e.

a_n=ra_{n-1}

Thus, substituting r = 1/5

\:a_n=\frac{1}{5}\left(a_{n-1}\right)  

and a₁ = 125.

Therefore, the Recursive Formula for the sequence is:

\:a_n=\frac{1}{5}\left(a_{n-1}\right)     ; a₁ = 125

Hence, option D is correct.

You might be interested in
To do linear regression, there must be paired scores on two variables.
kumpel [21]
True or False question, I would say that it's true.
7 0
3 years ago
Identify the property that justifies "x=y; if y=9, then x=9"
iragen [17]
I think the answer is substitution property of equality because you are substituting 9 for y as y=9.
3 0
3 years ago
Suppose you got 8 mangoes and 3 apples for $18 and 3 mangoes and 5 apples for $14.50. How much does each mango and each apple co
pshichka [43]

The mango costs $1.5 and the apple costs $2.

6 0
3 years ago
Find x Help ASAP ASAP
Blizzard [7]

the given figure is a rhombus, so it's area =

\frac{1}{2}  \times \: d1 \times d2

where, d1 and d2 are diagonals of the rhombus,

and since, the diagnonals of rhombus bisects each other, the values of their diagonals are

(2 × x) and (2 × 15) =》2x and 30 respectively,

so, by finding the area using the given diagonals and equating it with the real area, we get :

=》

\frac{1}{2}  \times 2x \times 30 = 300

=》

x \times 30 = 300

=》

x =  \frac{300}{30}

=》

x = 10

so,

value of x = 10 units

4 0
3 years ago
What is x, the length of the diagonal, to the nearest
love history [14]

The value of x, the length of the diagonal, to the nearest  whole number is 5

To get the value of x from the given diagram, we will use the cosine rule as shown:

c² = a² + b² - 2ab cos Ф

From the given diagram;

a  = 6

b = 4

Ф = 55 degrees

Substitute into the formula

c² = 6² + 4² - 2(4)(6)cos 55

c² = 36 + 16 - 48cos55

c² = 52 - 27.53

c² = 24.4

c = 4.94

c = 5 (to the nearest while number).

The value of x, the length of the diagonal, to the nearest  whole number is 5

Learn more on cosine rule here: brainly.com/question/7872492

8 0
2 years ago
Other questions:
  • PLEASE HELP GEOMETRY QUESTION!!
    15·1 answer
  • Victor always runs out of money by the end of the month, so he wants to start keeping a budget. Last month, he spent a total of
    8·1 answer
  • What does e=mc3 mean?
    9·1 answer
  • If f(x) = 4x, which statements are true of g(x)? Select two options.
    13·2 answers
  • 16a^2-4b^2 in factored form
    14·1 answer
  • I’m giving away 100 points please help :
    6·2 answers
  • A summer camp cookout is planned for the campers and their families. There is room for 200 people. Each adult costs 4, and each
    5·1 answer
  • Find the volume of the figure.
    9·1 answer
  • What is the value of the expression below when x=5?
    12·2 answers
  • Choose the correct term to complete the sentence.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!