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
Vlad [161]
3 years ago
8

Write the sum using summation notation, assuming the suggested pattern continues.

Mathematics
1 answer:
Ne4ueva [31]3 years ago
8 0

the first six terms of the sequence \bf a_1=-1\qquad a_n=2\times a_{n-1}

\bf \begin{array}{ccll}n&term&value\\\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\1&a_1&-1\\2&a_2&2\times a_{2-1}\\&&2\times a_1\\&&-2\\3&a_3&2\times a_{3-1}\\&&2\times a_2\\&&-4\\4&a_4&2\times a_{4-1}\\&&2\times a_3\\&&-8\\5&a_5&2\times a_{5-1}\\&&2\times a_4\\&&-16\\6&a_6&2\times a_{-1}\\&&2\times a_5\\&&-32\end{array}

now on this new edited version

\bf -8~~,~~\stackrel{-8+5}{-3}~~,~~\stackrel{-3+5}{2}~~,~~\stackrel{2+5}{7}....67

so, as you can see, the "common difference" of this arithmetic sequence is d = 5, hmmm what term is 67 anyway?

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\a_n=a_1+(n-1)d\qquad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\d=\textit{common difference}\\a_1=-8\\d=5\\a_n=67\end{cases}\\\\\\67=-8+(n-1)5\implies 67=-8-5+5n\implies 67=-13+5n\\\\\\80=5n\implies \cfrac{80}{5}=n\implies 16=n\qquad ~~~~~~~~~~\boxed{\sum\limits_{i=0}^{15}~-8+5i}

You might be interested in
Helpsssssssssssssss!!!!!!!!!!!!!!!!!!!!
serious [3.7K]

Answer:

the common differnence is positive 3

Step-by-step explanation:

its going back by 3 since its going back to 0 its positive

8 0
2 years ago
Read 2 more answers
Find the side length of the square
IgorLugansk [536]

the answer is 30.3

hope it helps

8 0
3 years ago
I am so confused. Can anyone help me??
natita [175]

Answer:

bro!  im in 7th grade i would try to help but im very stupid sorry for the dissopiontment

Step-by-step explanation:

8 0
3 years ago
A set of furniture was sold for GH cedis 3000 at a profit of 25%. Find the cost price.
Sindrei [870]

Answer:

<h2>2400GH Cedis </h2>

Step-by-step explanation:

Selling \:price = 3000gh Cedis\\Profit \% = 25\%\\Cost\:price =?\\\\CP =\frac{ ( Selling\:price \times 100 )}{ ( 100 + percentage profit)}  \\\\C.P = \frac{3000\times 100 }{100+25}\\\\ C.P = \frac{300000}{125} \\\\Cost\: Price = 2400gh Cedis

8 0
3 years ago
3. The amount was $120 at 5% rate for 4<br> years.
Inga [223]

Answer:

Go to photo math thank me later

Step-by-step explanation:

dowload tha app on ur phone

5 0
3 years ago
Other questions:
  • PLEASE URGENT I DONT WANNA FAIL
    10·1 answer
  • What is the answer to 20-3x=175
    5·2 answers
  • If she asks you to cut a strip of pie crust long enough to go around the outside of the pan
    10·1 answer
  • Give an example of when you would make a frequency table to solve a problem.
    14·1 answer
  • Show work for -3/5 x -5
    12·1 answer
  • What is the next three numbers in this pattern 10 5 20 10 40
    13·2 answers
  • PLS HELP I DONT UNDERSTAND :( WILL MARK BRAINLIEST+
    14·2 answers
  • Simplify the expression completely.
    6·2 answers
  • The circle below is centered at the point (-1, 2) and has a radius of length 3.
    13·1 answer
  • Is anyone else airpods not working like one ear not work and the case not charging​
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!