Question 39508: I really need some help!! (Fast!!!!) Please....
Using the index of a series as the domain an dthe value of the series as the range, is the series a function?
Include in ans:
Which one of the basic functions(linear, quadratic, rational, or exponential) is related to the arithmetic series?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?
Give real life examples of both arithmetic and geometric sequences and series. Explain how these might affect you personally?
2. Use the arithmetic sequence of numbers 2,4,6,8,10...to find the following:
a) What is d, the difference between any 2 terms?
Ans:
Show work below:
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Ans:
c) Using the formula for the sum of an aritmetic series, what is the sum of the first 20 terms?
Ans:
d) Using the formula for the sum of an aritmetic series, what is the sum of the first 30 terms?
Ans:
e)What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc..)?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Using the index of a series as the domain an dthe value of the series as the range, is the series a function?
Include in ans:
Which one of the basic functions(linear, quadratic, rational, or exponential) is related to the arithmetic series?TN=A+(N-1)*D.............LINEAR EQN.
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?TN=A*R^(N-1)............EXPONENTIAL
Give real life examples of both arithmetic and geometric sequences and series. Explain how these might affect you personally?
REAL LIFE EXAMPLES...
ARITHMATIC / PROGRESSION/SERIES....A.P.
SUPPOSE YOU ARE SAVING YOUR MONEY IN A BANK BY
SYSTEMATIC PLAN OF
DEPOSITING 100 $ A MONTH...THEN STARTING WITH A 100$
ACCOUNT YOUR
MONEY IN CREDIT WITHOUT INTEREST ,WOULD BE AN EXAMPLE
OF A.P...IT
WILL BE..... TAKING MONTH AS AN INDEX...
100,200,300,400......
GEOMETRIC PROGRESSION/SERIES.....G.P.
IN A SIMILAR WAY SUPPOSE YOU DEPOSITED 1000 $ IN A
BANK FOR INTEREST
OF 4% PER YEAR,AND THE INTEREST IS CALCULATED AT THE
END EVERY YEAR
AND ADDED TO THE PRINCIPAL,THEN THE AMOUNT GROWN AT
THE END OF YEAR IS
AN EXAMPLE OF G.P.TAKING YEAR AS N INDEX....THE AMOUNT
AT THE END OF
SUCCESSIVE YEARS IS .....
1000,1000*1.04,1000*1.04^2,1000*1.04^3....ETC...
KNOWING THAT A G.P WILL YIELD MORE THAN A.P. ,WE BETTER PUT OUR MONEY IN INTERESTING EARNING SECURITY THAN AT HOME WHERE NO INTEREST ACCRUES.
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SEE THE FOLLOWING EXAMPLE WHICH IS PRACTICALLY SAME
---------------------------------------------------
1)Use the arithmetic
sequence of numbers 2, 4, 6, 8, 10� to find the
following:
a)What is d, the difference between any 2 terms?
Answer:
Show work in this space.
b)Using the formula for the nth term of an arithmetic
sequence, what is 101st term? Answer:
Show work in this space.
c)Using the formula for the sum of an arithmetic
series, what is the sum of the first 20 terms?
Answer:
Show work in this space.
d)Using the formula for the sum of an arithmetic
series, what is the sum of the first 30 terms?
Answer:
Show work in this space.
e)What observation can you make about these sums of
this series (HINT: It would be beneficial to find a
few more sums like the sum of the first 2, then the
first 3, etc.)?
Answer:
1 solutions
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Answer 16520 by venugopalramana(1619) on 2006-03-10
07:41:16 (Show Source):
1)Use the arithmetic sequence of numbers 2, 4, 6, 8,
10� to find the following:
a)What is d, the difference between any 2 terms?
Answer:
Show work in this space.
D= COMMON DIFFERENCE BETWEEN 2 CONSECUTIVE TERMS
4-2=6-4=8-6=10-8=2....CONSTANT...THIS IS THE PROPERTY
OF ARITHMATIC PROGRESSION
b)Using the formula for the nth term of an arithmetic
sequence, what is 101st term? Answer:
Show work in this space.
TN=A+(N-1)D=2+(N-1)2=2N
T101=2*101=202
c)Using the formula for the sum of an arithmetic
series, what is the sum of the first 20 terms?
Answer:
Show work in this space.
SN=(N/2){2A+(N-1)D}=(N/2){2*2+(N-1)2}=(N/2)(2N+2)=N^2+N
S20=20^2+20=420
d)Using the formula for the sum of an arithmetic
series, what is the sum of the first 30 terms?
Answer:
Show work in this space.
S30=30^2+30=930
e)What observation can you make about these sums of
this series (HINT: It would be beneficial to find a
few more sums like the sum of the first 2, then the
first 3, etc.)?
Answer: 1.THE SUM IS A QUDRATATIC IN N.
2.IT IS EQUAL TO THE SUM OF NUMBER OF TERMS AND ITS
SQUARE
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