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
DIA [1.3K]
3 years ago
8

The first term of a geometric sequence is equal to a and the common ratio of the sequence is r.

Mathematics
1 answer:
ololo11 [35]3 years ago
4 0

Answer: (a)  {a, ar, ar², ar³, ar⁴, ar⁵...}, (b)  arⁿ⁻¹

For part (a), the question gives us the first term a, and then asks us to apply the common ratio r six times.

In order for ar = a, the nth term of r will have to equal 0 (this implies that n is an exponent; thus giving us the first term a, as r = 1).

Since we use this method on the first term, we must use it for the next five, in which r gains an additional exponent for every consecutive value (nth term) thereafter.  

Ultimately getting: {a, ar, ar², ar³, ar⁴, ar⁵...}

For part (b), we first have to understand that the sequence does not start at 0, but at 1 for n. In order for ar = a, with n = 1, there needs to be subtraction of -1 within the exponent. So that arⁿ⁻¹

If we check and apply this, we can see that:

{ar¹⁻¹, ar²⁻¹, ar³⁻¹, ar⁴⁻¹, ar⁵⁻¹, ar⁶⁻¹...} = {a, ar, ar², ar³, ar⁴, ar⁵...} = arⁿ⁻¹ = Tn

You might be interested in
John needs to divide the sample in half once the number of bacteria has reached 1000. How many hours after the initial time must
Reil [10]

Answer:

Option A

Step-by-step explanation:

The complete question is attached here

The rate of increase of bacterial population  be K

As we know

Y = Y_0 * e^{kT}

where Y is the final population. In this case it is 1000

K is the rate of increase of population i.e 3 times per hour

T is the time in hours

Y0 is the initial population = 5

Substituting the given values, we get -

1000 = 5 *e^{3*T}\\200 = e^{3*T}

Taking log on both sides, we get -

ln 200 = ln e^{3T}

2.718 * 2.301 = 3T

T = 2.084 hours

hence, option A is correct

8 0
3 years ago
9:00 oclock as a fraction in its lowest form​
kirill115 [55]

Answer:

1/9

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Find the 2 digit number from numbers 1 2 3 4 5 that divides into of 889.
atroni [7]

Answer:

Step-by-step explanation:

1 it have 8

2 it have 8

and have 9

is is hundreds so is 889 so they are 3 numbers in it

7 0
2 years ago
Kayla says that the point labeled C in the diagram below is the center. Raymond says that point C is the radius. A sphere. The c
liq [111]

Answer:

Kayla is correct; the center is a fixed point in the middle of the sphere.

Step-by-step explanation:

Kayla is correct. Raymond is wrong because a point cannot be a radius: a radius is a line segment from the center to the surface.

The center is the fixed point in the middle of the sphere.

6 0
3 years ago
Read 2 more answers
The area of triangle ABC is 1.89 square feet. The measure of side c is ______.
Feliz [49]

we are given

Area is 1.89

A=40

b=2.8

now, we can use area formula

A=\frac{1}{2} c*b*sin(A)

1.89=\frac{1}{2} *c*2.8*sin(40)

now, we can solve for c

we will get

c=2.10023.............Answer

7 0
3 years ago
Other questions:
  • Josie had a choice of three breads, three choices of meat, and five choices of cheese to make a sandwich. How many different san
    14·1 answer
  • Joanna works two days each
    10·1 answer
  • Anyone willing to answer this question?
    5·1 answer
  • How do I graph this.
    7·1 answer
  • The nth term of a sequence is 3(n + 3).
    8·1 answer
  • HELP IM TIMED it’s subtracting decimals
    15·2 answers
  • Which expressions are equivalent to 5 ( -2k - 3 ) + 2k?
    10·1 answer
  • Y = 3/5x + 5<br><br><br> y = -3/5x + 5<br><br><br> y = 3/5x - 5<br><br><br> y = -3/5x - 5
    9·2 answers
  • PLEASE AWNSER SOON IT'S DUE IN 10 MIN!
    14·2 answers
  • Multiply 6 times two-ninths.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!