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
Vinil7 [7]
2 years ago
6

BRAINLIEST AWARD NO.2

Mathematics
1 answer:
zzz [600]2 years ago
8 0

Answer:

A whole number first term to render as fifth term a value larger than 10000, should be at least 121

Step-by-step explanation:

The formula is given as recursive since it involves the previous number of the sequence, and defined as:

a_n=a_{n-1}*3+6

we also know that the first term is 4

Then in this case, the first five terms are:

a_1=4\\a_2=4*3+6=18\\a_3=18*3+6=60\\a_4=60*3+6=186\\a_5=186*3+6=564\\

So if we want to find the first term in the case that the fifth one is greater than 10,000 using this recursive formula, now we have to start backwards, and say that the fifth term is "> 10000" and what the fourth one is.

Notice that if you have this definition for the nth term, we can obtain from it, what the previous term is to find the general rule:

a_n=a_{n-1}*3+6\\a_n-6=a_{n-1}*3\\\frac{a_n-6}{3} = a_{n-1}\\a_{n-1}=\frac{a_n}{3} -2

So the rule is to subtract 6 from he term, and divide the subtraction by 3. Then working backwards:

a_5>10000\\\frac{a_5}{3} -2>\frac{10000}{3} -2\\a_4>=\frac{10000}{3} -2\\\frac{a_4}{3} -2>\frac{\frac{10000}{3}-2}{3}-2 =\frac{10000}{9}-\frac{8}{3} \\a_3>\frac{10000}{9}-\frac{8}{3} \\\frac{a_3}{3} -2>\frac{\frac{10000}{9}-\frac{8}{3} }{3} -2=\frac{10000}{27} -\frac{8}{9} -2=\frac{10000}{27} -\frac{26}{9}\\a_2=\frac{10000}{27} -\frac{26}{9}\\\frac{a_2}{3} -2>\frac{\frac{10000}{27} -\frac{26}{9}}{3} -2=\frac{10000}{81} -\frac{80}{27} \\a_1>\frac{10000}{81} -\frac{80}{27}\approx 120.49

therefore, the starting first term should be at least about 121 to give a fifth term larger than 10,000

You might be interested in
Zuri quickly solved the problem and told her team, "Hey! I go it m\large \angleA = 93°, m\large \angleB = 63°, m\large \angleC =
Step2247 [10]

Answer:

Mikaya and Olivia are correct to be suspicious

Step-by-step explanation:

Sum of the angles of a triangle is always 180

But, The sum of all angles of the triangle that Zuri solved = 93 + 63 + 36 = 192 ≠ 180

So, Zuri is wrong

8 0
2 years ago
The rate of discount, R, can be determined using the formula, where P is the regular price of an item and D is the discount or a
astraxan [27]

Answer:

B.0.31

Step-by-step explanation:

% of change = amount of change/original price

R=(P-D)÷P

39-27=12

12÷39=.307

≈.31

8 0
3 years ago
The random variable X is normally distributed. P(2045).
bekas [8.4K]
What the answer option
4 0
2 years ago
Solve the equation !!!!!!!
patriot [66]

Answer:

x= 5pi/4, 7pi/4

Step-by-step explanation:

7 0
2 years ago
Five friends each knit one part of a scarf that is 11 yards long. 12 Which shows the fractions of the scarf each friend could ha
kotegsom [21]

Answer:

2/12 + 3/12 + 3/12 + 2/12 + 5/12

Step-by-step explanation:

I hope I'm right

3 0
2 years ago
Other questions:
  • What grade does Lamont need to get on the next test to have an average of exactly 90? Explain your answer.
    15·1 answer
  • SImplify: ((x+3)/9)/((x+12/)6)
    13·1 answer
  • Which value should be added to this data set to produce a mean of 13?
    5·2 answers
  • Are these quadratic functions?
    10·1 answer
  • Given the following data: X 1 4 6 7 Y 9 7 8 1 a) Find the coefficient of correlation. b) Find the equation of the regression lin
    10·1 answer
  • Y varies inversely with x, and k (the constant of variation) = 1.24. What is the value of y when x = 4.96?
    12·1 answer
  • Which expression is equivalent to-2-7? Subraction with Intergers
    6·1 answer
  • Why is the power in the united states dived between several branches
    7·2 answers
  • Tyler says he invented a number puzzle.
    7·1 answer
  • Bill went on a very long run, so he ran kind of slowly. He ran 2 miles in 30 minutes. How many miles would he run in three hours
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!