Question

Choose seven consecutive terms in any arithmetic sequence and check that the arithmetic average (the sum...

Choose seven consecutive terms in any arithmetic sequence and check that the arithmetic average (the sum of the seven terms divided by 7) equals the middle term. Prove that the result is true for every arithmetic sequence. give me a paragraph to explain.

Math   Geometry   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Let 1,4,7,10,13,16,19 is an arithmetic sequence with common difference 3.

Arithmetic average = (1+4+7+10+13+16+19)/7

Arithmetic average = 70/7

Arithmetic average = 10 which is middle term.

To prove result in general :

X1,X2,X3,X4,X5,X6,X7 is an arithmetic sequence with common difference "a".

Then, X2 = X1+a

X3 = X1+2a

X4 = X1+3a

X5 = X1+4a

X6 = X1+5a

X7 = X1+6a

Arithmetic average = (X1+X2+X3+X4+X5+X6+X7)/7

Arithmetic average = (X1+X1+a+X1+2a+X1+3a+X1+4a+X1+5a+X1+6a)/7

Arithmetic average = (7X1+21a)/7

Arithmetic average = 7(X1+3a)/7

Arithmetic average = X1+3a

therefore arithmetic average is equal to middle term.

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Bonus Question. Give a complete proof in paragraph form. Any incorrect use of terms or symbols...
Bonus Question. Give a complete proof in paragraph form. Any incorrect use of terms or symbols will result in no credit. Any false or nonsensical statements will result in no credit. 12. (5 points (bonus)) Prove that for every even positive integer n, (1 − 1/2)(1 + 1/3)(1 − 1/4) · · · (1 − (−1)^n/n) = 1/2 .
We are given a sequence of numbers: 1, 3, 5, 7, 9, . . . and...
We are given a sequence of numbers: 1, 3, 5, 7, 9, . . . and want to prove that the closed formula for the sequence is an = 2n – 1.          What would the next number in the sequence be? What is the recursive formula for the sequence? Is the closed formula true for a1? What about a2? What about a3? Critical Thinking How many values would we have to check before we could be sure that the...
Review the   PILOT DOSE-RESPONSE STUDY OF MEMOROL Consent Form (ICF) Check  to determine whether the required ICH-GCP...
Review the   PILOT DOSE-RESPONSE STUDY OF MEMOROL Consent Form (ICF) Check  to determine whether the required ICH-GCP elements are present by checking Yes or No in the Informed Consent Form Checklist’. If you review an element and are not convinced that the ICF adequately covers the details– indicate this on the review form by making a note in the “comments section. Introduction: I have been asked to participate in a 1 month research study which will evaluate the effectiveness and safety...
Suppose that a city operates two neighborhood schools, one in the rich neighborhood and one in...
Suppose that a city operates two neighborhood schools, one in the rich neighborhood and one in the poor neighborhood. The schools are equal in size and currently have equal budgets. The city receives $10 million in federal grant money that can be used to supplement the budgets of the two schools, which are initially identical. For each school, the average score on a standardized achievement test depends on how many dollars are allocated to the school. Letting S denote the...
Suppose that a city operates two neighborhood schools, one in the rich neighborhood and one in...
Suppose that a city operates two neighborhood schools, one in the rich neighborhood and one in the poor neighborhood. The schools are equal in size and currently have equal budgets. The city receives $10 million in federal grant money that can be used to supplement the budgets of the two schools, which are initially identical. For each school, the average score on a standardized achievement test depends on how many dollars are allocated to the school. Letting S denote the...
PLEASE FILL IN THE BLANKS WITH THE PROPER TERM! THANKS Key Terms ---------------------------------------------------------------------------------------------------------------------------- Positive relationship ---...
PLEASE FILL IN THE BLANKS WITH THE PROPER TERM! THANKS Key Terms ---------------------------------------------------------------------------------------------------------------------------- Positive relationship --- Occurs in so far as pairs of observations tend to occupy similar relative positions in their respective distribution. Negative relationship --- Occurs in so far as pairs of observations tend to occupy dissimilar relative positions in their respective distribution. Scatterplot --- a graph containing a cluster of dots that represents all pairs of observations. Person correlation coefficient --- A number between –1 and +1...
Total utility can be objectively measured in numbers that indicate usefulness or benefit to the consumer....
Total utility can be objectively measured in numbers that indicate usefulness or benefit to the consumer. ____ 2. Consumers should purchase quantities of a good to the point where MU > P. ____ 3. Voluntary exchange requires that there must be mutual gain. ____ 4. Points along a budget line represent the maximum combinations of two commodities that a consumer can afford. ____ 5. The budget line represents a consumer's preferences for a commodity. ____ 6. A change in consumer...
CASE Wyatt Earp - The Buffalo Hunter F. Robert Jacobs, Indiana University The legend of Wyatt...
CASE Wyatt Earp - The Buffalo Hunter F. Robert Jacobs, Indiana University The legend of Wyatt Earp lives on largely based on his exploits as a gunfighter and Marshall of the frontier West in the 1880s. The classic tales of the shootout at the O.K. Corral in Tombstone or his sawed-off shotgun duel with Curly Bill are possibly the most celebrated gunfights of frontier history and cannot fail to stir the reader's imagination. Wyatt lived to be over 80 years...
1. What is an ISP (Integrated Service Provider) for supply chains? (1 point) A. A consultant...
1. What is an ISP (Integrated Service Provider) for supply chains? (1 point) A. A consultant agency which integrates the supply chain for companies B. A 2 PL or a 3PL, but not a 4PL C. A company supplying transportation and warehousing services D. A logistics service company specialized in suppling VAS (value added services) 2. What characterizes a 4 PL? (1 point) A. They are non-asset based and provides integrated services primarily supplied by asset based providers, for example...
2. A demand curve indicate a. the maximum willingness to pay for a given quantity b.the...
2. A demand curve indicate a. the maximum willingness to pay for a given quantity b.the consumer's gain from exchange c.the market price of a good or service d. the equilibrum quantity 3. trade permitts countries to a. consume more than they capable of producing b.produce based on their comparative advantage c.specialize more fully d.all of above 4. which of the following dose not impact how elastic supply is? a. whether the supply is local or global b.the share of...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT