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
earnstyle [38]
2 years ago
12

Write the sum using summation notation, assuming the suggested pattern continues. 6, -18, 54, -162, +… Is this sequence arithmet

ic or geometric? Explain your answer.
Mathematics
1 answer:
telo118 [61]2 years ago
7 0

Answer:

Hello,

This sequence is geometric with a ratio of -3

the first term is 6

Step-by-step explanation:

u_1=6\\u_2=-18=6*(-3)=u_1*(-3)\\u_3=54=-18*(-3)=u_2*(-3)=u_1*(-3)^2\\u_4=-162=u_3*(-3)=u_1*(-3)^3\\\\...\\u_{n+1}=u_1*(-3)^n\\\\\displaystyle \sum\limits^\infty _{i=1}u_i = \lim_{n \to \infty} \sum\limits^n _{i=1}u_1*(-3)^{i-1}\\=6*\lim_{n \to \infty} \sum\limits^\infty _{i=1}(-3)^{i-1}\\=6*\frac{1-(-3)^n}{1-(-3)} \\=\dfrac{3}{2} *({1-(-3)^n)\\

serie does not converge.

You might be interested in
Tarantulas are one of the largest spiders on Earth. A
nlexa [21]
Tarantulas are 5.9 centimeters longer.
3 0
2 years ago
I need help I’m bad at math
Alina [70]
If you'd graph this function, you'd see that it's positive on [-1.5,0], and that it's possible to inscribe 3 rectangles on the intervals [-1.5,-1), (-1,-0.5), (-0.5, 1].

The width of each rect. is 1/2.

The heights of the 3 inscribed rect. are {-2.25+6, -1+6, -.25+6} = {3.75,5,5.75}.

The areas of these 3 inscribed rect. are (1/2)*{3.75,5,5.75}, which come out to:

{1.875, 2.5, 2.875}

Add these three areas together; you sum will represent the approx. area under the given curve on the given interval:  1.875+2.5+2.875 = ?
5 0
3 years ago
What is a function exponential
valkas [14]
(Credit goes to google)<span>f ( x ) = a </span>x<span>. where x is a variable, and a is a constant called the base of the </span>function<span>. The most commonly encountered </span>exponential-function<span> base is the transcendental number e , which is equal to approximately 2.71828.</span>
3 0
3 years ago
Read 2 more answers
Milena just turned 11 years old. How old was she 2 1/4 years ago?
ankoles [38]
Milena was 9 years and 3 months old
5 0
3 years ago
Read 2 more answers
last year Rafael opened an investment was count with $5,500 at the end of the year the amount in the account has been decreased
Vlad1618 [11]

Answer: The new amount is 0.78*5500. Which is 4290. The decrease is 5500-4290=1210.

5 0
2 years ago
Other questions:
  • what are the coordinates of thee point (-10,-3) after a 180 degree clockwise rotation about the origin?
    10·2 answers
  • The low temperatures for a week in Edmonton, Alberta are -15 C, -12 C, -10 C, -12 C, -18 C, -20 C, and -25 C. What is the mean l
    9·1 answer
  • Divide use partial quotients 6 divided by 258
    9·1 answer
  • The city limits of Las Pythagoras form a perfect shape of an isosceles right triangle whose legs are both
    14·1 answer
  • Please answer any one them thank you so much
    5·2 answers
  • ANSWER PLS!!!!!!!!!!!!!!!!!!!!
    5·2 answers
  • Which is better buy? 5 lb of flour for $0.90 or<br> 8 lb for $1.25
    14·2 answers
  • If your answer is b<img src="https://tex.z-dn.net/?f=%5Cneq" id="TexFormula1" title="\neq" alt="\neq" align="absmiddle" class="l
    10·1 answer
  • Which equations are correct? select three options. n = 10 n = 7 cf = 59 fe = 42 cd = 30
    12·1 answer
  • What is the answer of 2 x ____ = -7.7
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!