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
aleksandr82 [10.1K]
2 years ago
6

Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5

Mathematics
1 answer:
zaharov [31]2 years ago
7 0

Answer:

31

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}} or \displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}

Therefore, the solution is 31.

__________________________________________________________

Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as \displaystyle \large{a_{n-1} \cdot r = a_n} meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:

\displaystyle \large{r=\frac{a_{n+1}}{a_n}}

Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:

\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}\\\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}

Above should be applied for series that have common ratio not equal to 1.

\displaystyle \large{S_n=a_1 \cdot n}

Above should be applied for series that have common ratio exactly equal to 1.

__________________________________________________________

Topics

Sequence & Series — Geometric Series

__________________________________________________________

Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

__________________________________________________________

You might be interested in
Eva has £6.05 in her moneybox.
PIT_PIT [208]

Answer:

11 of 20p, 22 of 10p and 33 of 5p

Step-by-step explanation:

Eva has 20p, 10p and 5p coins, total of £6.05 = 605p

Let 20p=x, 10p=y, 5p=z

<u>Then</u>:

  • 20x + 10y + 5z = 605
  • y : x = 2 : 1 ⇒ x= y/2
  • y : z = 2 : 3 ⇒ z= 3y/2

<u>Rewriting the first equation considering next two:</u>

  • 10y + 10y + 7.5y = 605
  • 27.5y = 605
  • y= 605/27.5
  • y= 22
  • x= y/2 = 22/2 = 11
  • z = 3y/2 = 3*11 = 33

<u>Answer:</u> 11 of 20p coins, 22 of 10p coins and 33 of 5p coins

3 0
3 years ago
Multiply (−4) × (−2) × (−5).
babunello [35]

Answer: -40 or negative forty

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
A workers regular hourly rate of pay is $13. What is the workers total pay for working 40 regulars and 3 hours overtime at a rat
ANTONII [103]

Answer:

578.50

Step-by-step explanation:

The worker worked 40 hours at 13 dollars

40 * 13 =520

Then they worked 3 hours at 13(1.5) or 19.50

3*19.50 =58.5

The total amount of money earned is regular time plus overtime

520 + 58.5 =578.50

3 0
3 years ago
What is<br> -3/4 + 2 3/4
Fittoniya [83]

Answer:

2

Step-by-step explanation:

ok so let's start

were starting off with -3/4 and were adding 2 3/4 to that and it's equal to 2 3/4 subtract 3/4

-3/4 + 2 3/4 = 2 3/4 - 3/4

2 3/4 - 3/4 = 2

-3/4 + 2 3/4 = 2

it's 2 my dude or girl i don't know

3 0
3 years ago
What is 3 multiplied by 1 8/11 as a mixed number or fraction
marishachu [46]

Answer:

57/11 or 5 2/11

Step-by-step explanation:

Convert 1 8/11 into an improper fraction:  1 8/11 = 19/11.

Next, multiply this 19/11 by 3, obtaining 57/11.

This mixed numer is an improper fraction.  

If you wish to go further, convert 57/11 into a mixed number:

57/11 = 5 2/11

4 0
3 years ago
Read 2 more answers
Other questions:
  • What type of graph organizes data into 4 groups of equal size, and is often used to compare two sets of data.
    5·1 answer
  • (04.02 MC)
    12·2 answers
  • Find the of this circle in terms of pi
    14·2 answers
  • Need help with all will mark you BRAINLY-EST THNX​
    5·1 answer
  • Eliza is a chef at a restaurant. she is making spaghetti sauce and put 14 tomatoes and 4 onions in the pot. what is the ratio of
    11·1 answer
  • Solve<br> Sin(2theta)=1/2
    10·1 answer
  • Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function:
    6·1 answer
  • PLEASE HELP. WILL GIVE BRAINLIEST
    11·2 answers
  • Rapunzel makes $5.78 per hour. Gretta makes $15.46 per hour. How
    13·2 answers
  • Factor 7x3y4−7x2y5 completely.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!