Question 87087: 1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… 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:
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c) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms?
Answer:
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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 2 to 4, 4 to 6, 6 to 8, and 8 to 10 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 10: I'm going to subtract 8 from it (which is the previous term) to get a difference of 2. If I pick 8, and subtract 6, 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 2 (the 1st term) and I go to 4, this means I increase by 2 each term. If I let n=0 then the term is 2, and if I let n=1 then the term is 4. This basically tells me that the arithmetic sequence is 2n+2. To verify, simply plug in the 1st term (n=0) and you'll get 2. Plug in the 2nd term (n=1) you'll get 4, if I let n=2 I get 6, etc. If I wanted to know the 101st term, let n=100 (remember zero is the first term) and it comes to
 So the 101st term is 202
c)Now lets find the sum of the first 20 terms
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
Since we know the first term is 2, we know that  .
So lets calculate the 20th term.
Let n=19(remember we started at n=0)
So the term 
Now lets evaluate the sum
 Plug in values.
 Simplify
 So the sum of the first 20 terms is 420.
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