SOLUTION: use the arthimetis sequence of numbers 1,3,5,7,9,... to find the following what is d, the difference between any 2 terms? show work Using the formula for the nth term of an ar

Algebra ->  Sequences-and-series -> SOLUTION: use the arthimetis sequence of numbers 1,3,5,7,9,... to find the following what is d, the difference between any 2 terms? show work Using the formula for the nth term of an ar      Log On


   



Question 73070: use the arthimetis sequence of numbers 1,3,5,7,9,... to find the following what is d, the difference between any 2 terms? show work

Using the formula for the nth term of an arthimetoc sequence, what is the 101st term? show work?
Using the formula for the sum of an arthimetic sequence, what is the sum of the first 20 terms? show work
Using the formula for the sum of an arthimetic sequence, what is the sum of the first 30 terms? show work

Answer by rmromero(383) About Me  (Show Source):
You can put this solution on YOUR website!

Use the arthimetis sequence of numbers 1,3,5,7,9,... to find the following what is d, the difference between any 2 terms? show work


d = 3 - 1
= 2
Using the formula for the nth term of an arthimetoc sequence, what is the 101st term? show work?
a%5B1%5D+=+1
d = 2
n = 101
a%5Bn%5D+=+a%5B1%5D+%2B+%28n+-+1%29d
a%5Bn%5D+=+1+%2B+%28101+-+1%292
a%5Bn%5D+=+1+%2B+%28100%292
a%5Bn%5D+=+1+%2B+200
a%5Bn%5D+=+201
Using the formula for the sum of an arthimetic sequence, what is the sum of the first 20 terms? show work
a%5B1%5D+=+1
d = 2
n = 20
n
S%5Bn%5D = ___ %28a%5B1%5D+%2B+a%5Bn%5D%29
2

Let us find a%5Bn%5D first:
a%5Bn%5D+=+a%5B1%5D+%2B+%28n+-+1%29d
a%5Bn%5D+=+1+%2B+%2820+-+1%292
a%5Bn%5D+=+1+%2B+%2819%292
a%5Bn%5D+=+1+%2B+38
a%5Bn%5D+=+39

20
S%5Bn%5D = ___ %281+%2B+39%29
2

S%5Bn%5D = 10 (40)
= 400

Using the formula for the sum of an arthimetic sequence, what is the sum of the first 30 terms? show work
a%5B1%5D+=+1
d = 2
n = 30
n
S%5Bn%5D = ___ %28a%5B1%5D+%2B+a%5Bn%5D%29
2

Let us find a%5Bn%5D first:
a%5Bn%5D+=+a%5B1%5D+%2B+%28n+-+1%29d
a%5Bn%5D+=+1+%2B+%2830+-+1%292
a%5Bn%5D+=+1+%2B+%2829%292
a%5Bn%5D+=+1+%2B+58
a%5Bn%5D+=+59

30
S%5Bn%5D = ___ %281+%2B+59%29
2

S%5Bn%5D = 15 (60)
= 900