SOLUTION: please help...thanks 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: Show work in thi

Algebra ->  Sequences-and-series -> SOLUTION: please help...thanks 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: Show work in thi      Log On


   



Question 53424: please help...thanks
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:
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.)? Express your observations as a general formula in "n."
Answer:

Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
The difference between 2 terms is 2.
The nth term is, according to the formula:
a%5Bn%5D+=+a%5B1%5D+%2B+d%28n-1%29.
a%5B100%5D+=+1+%2B+2%28101+-+1%29+=+201
The sum of the first n terms is, according to the formula:
S%5Bn%5D+=+%28n%2F2%29%28a%5B1%5D+%2B+a%5Bn%5D%29
S%5Bn%5D+=+%28n%2F2%29%28a%5B1%5D+%2B+a%5B1%5D+%2B+d%28n-1%29%29
S%5B20%5D+=+10%281+%2B+1+%2B+2%2A19%29
S%5B20%5D+=+400
S%5B30%5D+=+15%281+%2B+1+%2B+2%2A29%29
S%5B30%5D+=+15%2A60
S%5B30%5D+=+900
If you calculate S%5Bn%5D for n from 1 to 10, you'll see that:
S%5Bn%5D+=+n%5E2