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
Wittaler [7]
2 years ago
14

The fourth term of an exponential sequence is 108 and the ratio is 3 . Calculate the value of the eighth term of the sequence, c

alculate the sum of the first five terms of the sequence.
Mathematics
1 answer:
Over [174]2 years ago
8 0

Answer:

8th term = 8748 , Sum of 5 terms = 484

Step-by-step explanation:

Formula for nth term in an exponential sequence = a r^ (n-1)

Here : n = 4 , ratio r = 3 ; And nth ie 4th number = 108

So,  a r^ (n-1) = nth item implies that → a 3 ^ (4-1) = 108

a 3^3 = 108 →  27 a = 108 → a = 108 / 27 → a = 4

<u>8th</u><u> term </u>= a r^ (n-1) , at  n = 8.  So, = 4 3^(8-1) = 4 3^7 = 4 x 2187 = 8748

Sum of n terms = a [(r^n) -1 ] / [r - 1] → <u>Sum </u><u>5</u><u> </u>terms = 4 [ (3^5)- 1] / [3 - 1]

= 4 [ (243) - 1] / 2 ] = 2 x 242 = 484

You might be interested in
Max is scuba diving at elevation of -64.5 feet, when friend signals to come higher. Max makes 2 ascents, each an equal distance
KengaRu [80]

Answer: - 42.95 feet

Explanation:

Let each ascent be x. Thus,

2 equal ascents = 2x

From the information given,

initial position = - 64.5 feet

Final position after 2 ascents = - 21.4 feet

This means that

- 64.5 + 2x = - 21.4

2x = - 21.4 + 64.5

2x = 43.1

x = 43.1/2

x = 21.55

Thus, Max's elevation after the first ascent is

- 64.5 + 21.55

= - 42.95 feet

4 0
1 year ago
What is 15/1/20 as a improper fraction
Lera25 [3.4K]
I'm not sure what you mean, but if you mean 15 and 1/20th, you just multiply 15 by 20 and add one which is 301 and keep the denominator
3 0
4 years ago
A grinding stone completes 175 revolutions before coming to a stop. How many radians did the stone complete
alexandr402 [8]

Answer:

175 * 2 * \pi

350\pi radians

Step-by-step explanation:

8 0
3 years ago
Otis plans to make 3 batches of sidewalk chalk How much plaster of paris does he need
den301095 [7]

Answer:

4\frac{1}{2} cups plaster of paris.

Step-by-step explanation:

Given:

for one batch of sidewalk chalk = 1\frac{1}{2} cup plaster of paris.

Number of bathes = 3

We need to find quantity of plaster of paris.

Solution:

For making 1 batch of sidewalk chalk = 1\frac{1}{2} cup plaster of paris.

For making 3 batches of sidewalk chalk = 3\times 1\frac{1}{2} cup plaster of paris.

= 3\times \frac{2\times 1+1}{2}

= 3\times \frac{2+1}{2}

= 3\times \frac{3}{2}

= \frac{3\times 3}{2}

= \frac{9}{2}

=4\frac{1}{2}

Therefore, he needed 4\frac{1}{2} cups plaster of paris.

5 0
3 years ago
A segment with endpoints A(2,6) and C(5,9) is partitioned by a point B such that AB and BC form a 3:1 ratio. Find B​
Aneli [31]

Answer:

The coordinate of point B is (4, 8.25)

Step-by-step explanation:

Here, we want to find the coordinates of point B

To do this, we are to use the section internal division formula as follows;

(x,y) = (nx1 + mx2)/(m + n) , (ny1 + my2)/(m + n)

In this case;

(x1,y1) = (2,6)

(x2,y2) = (5,9)

(m,n) = (3,1)

Substituting these values into the section formula, we have;

(x,y) = (1(1) + 3(5))/(1 + 3) , (1(6) + 3(9))/3 + 1)

(x,y) = (16/4, 33/4)

(x,y) = (4,8.25)

3 0
3 years ago
Other questions:
  • A car travels 240 miles in 4 hours. at this rate, how many miles will it travel in 8 hours
    10·1 answer
  • Which employee's path is the critical path on this activity graph? Explain how you know that this employee's path is the critica
    13·1 answer
  • What is this proper scientific notation for 0.000476?
    9·1 answer
  • Divide 33 Photos into two groups so the ratio is 4 to 7
    15·1 answer
  • the point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = (x – 12). What is the stand
    9·1 answer
  • A recipe calls for 2 1/2 tablespoons of oil and 3/4 tablespoons of vinegar. What is the ratio of oil to vinegar in this recipe?
    10·1 answer
  • 975 and is increasing at a rate of 2.5% per year for 7 years
    10·1 answer
  • the question is: The endpoints of ST are S(2,-2) and T(4,2) what are the coordinates of midpoint of ST?​
    13·1 answer
  • Gen ALL in Learning Show Summary Text to Speech (on) Previous Next &gt; 6 Line / is shown on the coordinate grid below. y Q1 Que
    9·1 answer
  • The percentage increase in the area of a rectangle if each of its sides is increased by 20% is.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!