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Question 44039This question is from textbook
: Please help me solve the following problems. I've tried to solve the problem but I don't it correct.
1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a)What is d, the difference between any 2 terms?
Answer:
d = 2
Show work in this space.
3-1=2
5-3=2
b)Using the formula for the nth term of an arithmetic sequence, what is 101st term?
Answer:
an = 1 + (n - 1)2
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:
Sum a20 = 400
Show work in this space
Sum an = n[2a1 + (n - 1)d] / 2
Sum a20 = 20[2 + (20 - 1)2] / 2
Sum a20 = 10[2 + (20 - 1)2]
Sum a20 = 10[2 + (19)2]
Sum a20 = 10[2 + 38]
Sum a20 = 10[40]
Sum a20 = 400
d)Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?
Answer:
Sum a20 = 900
Show work in this space
Sum an = n[2a1 + (n - 1)d] / 2
Sum a20 = 30[2 + (30 - 1)2] / 2
Sum a20 = 15[2 + (30 - 1)2]
Sum a20 = 15[2 + (29)2]
Sum a20 = 15[2 + 58]
Sum a20 = 15[60]
Sum a20 = 900
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.)? Express your observations as a general formula in "n."
Answer:
N an Sum
1 1
2 3 4
3 5 9
4 7 16
5 9 25
6 11 36
7 13 49
8 15 64
9 17 81
The sum of the nth in the series is the square of n.
This question is from textbook
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! SEE MY COMMENTS BELOW
Please help me solve the following problems. I've tried to solve the problem but I don't it correct.
1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a)What is d, the difference between any 2 terms?
Answer:
d = 2....CORRECT
Show work in this space.
3-1=2.......7-5=9-7=2...C.D.IS CONSTANT =2..HENCE A.P.
5-3=2
b)Using the formula for the nth term of an arithmetic sequence, what is 101st term?
Answer:
an = 1 + (n - 1)2
Show work in this space.
A101=1+(101-1)*2=1+200=201
c)Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Answer:
Sum a20 = 400..........PERFECT..
Show work in this space
Sum an = n[2a1 + (n - 1)d] / 2
Sum a20 = 20[2 + (20 - 1)2] / 2
Sum a20 = 10[2 + (20 - 1)2]
Sum a20 = 10[2 + (19)2]
Sum a20 = 10[2 + 38]
Sum a20 = 10[40]
Sum a20 = 400
d)Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?
Answer:
Sum a20 = 900..................EXCELLENT
Show work in this space
Sum an = n[2a1 + (n - 1)d] / 2
Sum a20 = 30[2 + (30 - 1)2] / 2
Sum a20 = 15[2 + (30 - 1)2]
Sum a20 = 15[2 + (29)2]
Sum a20 = 15[2 + 58]
Sum a20 = 15[60]
Sum a20 = 900
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.)? Express your observations as a general formula in "n."
Answer:
N an Sum
1 1
2 3 4
3 5 9
4 7 16
5 9 25
6 11 36
7 13 49
8 15 64
9 17 81
The sum of the nth in the series is the square of n. OUTSTANDING!!!
YOU DID OUTSTANDING JOB..WHY ARE YOU HAVING DOUBT!!BE CONFIDENT
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