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
FromTheMoon [43]
3 years ago
12

Part 1: Create a scenario for an arithmetic sequence. For example, Jasmine practices the piano for ______ minutes on Monday. Eve

ry day she ___________ her practice time by _________.
If she continues this pattern, how many minutes will she practice on the 7th day? Be sure to fill in the blanks with the words that will create an arithmetic sequence.

Use your scenario to write the function for the 7th term in your sequence using sequence notation.

Part 2: Create a scenario for a geometric sequence. For example, Anthony goes to the gym for ______ minutes on Monday. Every day he _________his gym time by ____________.

If he continues this pattern, how many minutes will he spend at the gym on the 5th day? Be sure to fill in the blanks with the words that will create a geometric sequence.

Use your scenario to write the formula for the 5th term in your sequence using sequence notation.

Part 3: Use your scenario from part 2 to write a question that will lead to using the geometric series formula. Use the formula to solve for Sn in your scenario.
Mathematics
1 answer:
mr Goodwill [35]3 years ago
6 0
Let a_n be the n'th term of a sequence, 

for example a_1 is the first term, a_2 is the second term and so on.
----------------------------------------------------------------------------------------------------
a sequence is arithmetic if the difference between any 2 terms is equal:

so an arithmetic sequence, for the first term = t, and the common difference = d, has the following form:

a_1=t

a_2=t+d

a_3=t+d+d

a_4=t+d+d+d

so clearly a_n=t+d*(n-1)
---------------------------------------------------------------------------------------------------
A sequence is geometric, if the ratio between any 2 consecutive terms is the same, and it is called the common ratio.

a geometric ratio with first term = t, and common ratio = r is:

a_1=t

a_2=t*r

a_3=t*r*r

a_4=t*r*r*r

thus clearly a_n=t* r^{n-1}
--------------------------------------------------------------------------------------------------

Part 1:

"<span>Jasmine practices the piano for  __30___ minutes on Monday. Every day she ____increases_______ her practice time by ____5 minutes_____. </span>"


let a_n be the number of hours Jasmine practices the n'th day, 

for n=7, t=30, d=5 we have

a_7=30+5*(7-1)=30+5*6=30+30=60,
 
minutes is the time Jasmine practices on the 7the day.


Part 2

 "<span>Anthony goes to the gym for ___60___ minutes on Monday. Every day he ___increases______his gym time by ____1/10_of the previous day_____. </span>"

if S_n represents the minutes that Anthony goes to gym on the n'th day, 

then

S_1=60

S_2=60+1/10*60=10/10*60+1/10*60=11/10*60=1.1*60

S_3=1.1*1.1*60

S_4=1.1*1.1*1.1*60

S_5=1.1*1.1*1.1*1.1*60= (1.1)^{4}*60= 1.4641*60=87.85
 (minutes)

Part 3: it is clear that the formula that can be derived in Part 2 is:

S_n=60*(1.1)^{n-1}

so assume we want to find how many hours does Anthony spend in the gym on the 10th day,

then we calculate S_10=60*(1.1)^{9}=60*2.358=141.5  (minutes)





You might be interested in
Lea is making a mosaic picture that is 3/4 foot tall and 11/12 foot wide what is the area of her mosaic
Fudgin [204]
Not enough info. But assuming it’s a rectangular, area = length * width
3/4*11/12 = 33/48 = 11/16 square feet
4 0
3 years ago
An obtuse triangle has a side length of $16,$ and a side length of $21.$ The third side length is also a positive integer. How m
Ymorist [56]

Answer:

3

Step-by-step explanation:

3 0
3 years ago
Pls, look at the picture for the question.
Kobotan [32]

Answer:

Step-by-step explanation:

Answer

When you put this into your calculator, you get - 7.2111. The closest point to that is L.

Answer: -7.2111 is closest to L

7 0
2 years ago
Read 2 more answers
48 is what percent of 120?
Nataliya [291]

Answer:

Step-by-step explanation:

57.6

8 0
2 years ago
Read 2 more answers
A question from my math class:
valina [46]

Answer:

A) $29.68

B) $5.60

Step-by-step explanation:

<u>Part A Explanation)</u>

To find the total cost including tax, you must multiply the total cost by .06 because .06 out of 1 is 6%. <em>Quick explanation on percentages.</em>

<u><em>DO NOT FORGET TO ADD THE TOTAL COST</em></u>

28.00 + (28.00 * .06) = 29.68

<u>Part B Explanation)</u>

This is asking only for the tip, not including the total cost. However, we need the total cost to calculate the tip.

28.00 * .20 = 5.6

<em>.20 out of 1 is 20%</em>

7 0
3 years ago
Other questions:
  • In the following line of letters, what letter follows the seventh E? B E F B E B I E F S E E D P F E S J E E J D E D E P J E T
    11·2 answers
  • Samir begins riding his bike at a rate of 6 mph. Twelve minutes later, Chris leaves from the same point and bikes along the same
    13·2 answers
  • If Zach checks his pulse for 2 minutes, what is his rate if he counts 162 beats?
    6·1 answer
  • Solve the solution for Y. 20 X+5Y=15
    14·1 answer
  • Students in a science class are divided into 6 equal groups with at least 4 students in each group for a project. Write and solv
    15·2 answers
  • Which ordered pair is a solution to the equation 3x-3y=21?
    10·1 answer
  • Three kitchen timers are set to start at the same time. The first goes off every 10 minutes, the second goes off every 15 minute
    13·1 answer
  • Three same-sized cubes are attached to the top of a rectangular prism as shown below. If a = 13 cm, b = 21 cm, and c = 3 cm, wha
    10·1 answer
  • I really need help with this one! please help me!
    6·1 answer
  • A barrel contains n cabbages which are either green or
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!