Question 29783: 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:
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b)Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:
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c)Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Answer:
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d)Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?
Answer:
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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:
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! 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:
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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:
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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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