SOLUTION: We are having a lecture this afternoon and I would like to be able to apply the lecture to this so that I can understand it. Thanks for any help.
1) Use the arithmetic sequenc
Algebra.Com
Question 83716: We are having a lecture this afternoon and I would like to be able to apply the lecture to this so that I can understand it. Thanks for any help.
1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a) What is d, the difference between any two consecutive 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 sequence, 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 sequence, 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 sequence (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:
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a) What is d, the difference between any two consecutive terms?
Answer:
Show work in this space
d is the difference between any term and its previous term
d=3-1 = 2
----------------------
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:
Show work in this space.
nth term = a(n) = a(1)+(n-1)d
a(101) = 1 + 100*2 = 201
------------------
c) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms?
Answer:
Show work in this space
S(n) = (n/2)(a(1)+a(n))
S(20) = (20/2)( 1 + a(20))
S(20) = 10(1+1+19*2)
S(20 = 10(40) = 400
--------------------
d) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms?
Answer:
Show work in this space
S(30) = 15(1+1+29*2)
S(30) = 15(60) = 900
--------------------
e) What observation can you make about these sums of this sequence (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:
The sums are obviously increasing.
I listed the formula.
======================
Cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)
The difference is the factor between each term. So going from 1 to 3, 3 to 5, 5 to 7, you see that its adding 2 each time. To verify, pick one term and subtract the previous term from it. So lets say I choose 7: I'm going to subtract 5 from it to get a difference of 2. If I pick 5, and subtract 3, I get a difference of 2.So the difference is: d=2
b)
Using what we found earlier, I know that the sequence counts up by 2 each term. So if I'm at 1 (the 1st term) and I go to 3, this means I increase by 2 each term. If I let n=0 then the term is 1, and if I let n=1 then the term is 3. This basically tells me that the arithmetic sequence is 2n+1. To verify, simply plug in the 1st term (n=0) and you'll get 1. Plug in the 2nd term (n=1) you'll get 3, if I let n=2 I get 5, etc. If I wanted to know the 101st term, let n=100 (zero is the first term) and it comes to
So the 101st term is 201
c)
Using the sum of arithmetic series formula:
a[1]=first term, a[n]=nth term (ending term which is the 20th term), and n is the number of terms
Plug in values
Simplify
So the sum of the first 20 terms is 400.
d)
Again using the same formula
a[1]=first term, a[n]=nth term (ending term which is the 30th term), and n is the number of terms
Plug in values
Simplify
e)
This one is a little tricky to explain, but the series (partial sums) follow the sequence (notice how each sum is a perfect square). To make a long story short, this sequence is the sum of odd integers. If you want the derivation check out
http://planetmath.org/encyclopedia/SumOfOddNumbers.html
RELATED QUESTIONS
I missed a lecture hour for my math class and I have no idea what to do on this... (answered by ankor@dixie-net.com,stanbon)
I have been having difficulty even just setting up the proper equation from this word... (answered by ankor@dixie-net.com)
Are the events
"the mode of the class is a lecture" and
"the type of a class is... (answered by fractalier)
Please suggest the null and alternative hypothesis for the following problem.
At... (answered by Theo)
Okay, I am in a basic math class at the Art Institute online. I do not want the answer... (answered by Alan3354)
Hi I am studting logarithms today with an exam tommorow.Unfortunatly i missed the... (answered by rapaljer,jsmallt9)
HELP!! Please!! Missed lecture and nothing makes sense. The following apply for the... (answered by funmath)
Hello, please i need assistant in solving this question
A survey found that 78% of the... (answered by Theo)
I have been asked to make f the subject from the following equation: v=u+ft/m. This is... (answered by stanbon)