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
Quadrilateral ABCD undergoes a reflection across the x-axis to form quadrilateral a b c d the coordinates of a r the reflected q
Zina [86]

Solution :

From the figure,

The coordinates of --

A = (-5,-3)

B = (-6,-1)

C = (-3,-1)  

D = (-2,-3)

When it undergoes reflection about x-axis, we have the coordinates of the quadrilateral as

A' = (-5,+3)

B' = (-6,+1)

C' = (-3,+1)

D' = (-2,+3)

Now A'B'C'D' is translated 3 units to right, so the coordinates will be --

A" = (-2,3)

B" = (-3,1)

C" = (0,1)

D" = (1,3)

When the quadrilateral moves third and two units up, we get

A"' = (3,3)

B"' = (2,1)

C"' = (5,1)

D"' = (6,3)

3 0
3 years ago
A) Ava made some money babysitting last week. She
GenaCL600 [577]
She made $40 last week because if you divide 80/2 it gives you 40. Because you are still counting the $5 she had spent.
8 0
3 years ago
Unit 8: Right Triangles & Trigonometry Homework 3
Genrish500 [490]
Can you post the image because I need to clarify in your trigonometry hw
5 0
3 years ago
The _____ of an angle is the ratio of the adjacent leg length to the hypotenuse length.
nlexa [21]

Answer:cosine ,just answered in apex


Step-by-step explanation:


4 0
3 years ago
Read 2 more answers
A charter bus travels 225 miles in
xz_007 [3.2K]

D because y (time spent) = 50 × x (distance travelled)

225÷4.5=50

x÷y=50

5 0
2 years ago
Other questions:
  • You start driving north for 7 miles, turn right, and drive east for another 24 miles. At the end of driving, what is your straig
    9·1 answer
  • Three instructors are comparing scores on their finals; each had 99 students. In Class A, one student got 1 point, another got 9
    12·1 answer
  • I need help please !!!!!
    8·1 answer
  • Which expression is equivalent to 1−2/3^−3 ?
    5·1 answer
  • Please answer correctly, will mark brainliest. If you dont know the answer please dont answer with idk or some other spam. Thank
    9·1 answer
  • The area of the sector of a circle of radius r/2 and central angle 2θ is __________
    7·1 answer
  • Solve for x.<br><br> x<br> 18<br> = 10<br><br> A) 8 <br> B) 28 <br> C) 162 <br> D) 180
    9·2 answers
  • A triangle has side lengths 11, 12, and 15. Is it acute, obtuse, or right?
    14·1 answer
  • Triangle ABC, shown in the diagram below, is an isosceles triangle.
    6·1 answer
  • Two rabbits land on deserted Salt Island; they breed,and the number of rabbits on the island doubles every 4 weeks. Two other ra
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!