Question 87087
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
{{{2*highlight(100)+2=202}}} So the 101st term is 202



c)Now lets find the sum of the first 20 terms


Using the sum of arithmetic series formula:
{{{s=(n/2)*(a[1]+a[n])}}} 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 {{{a[1]=2}}}. 

So lets calculate the 20th term. 


Let n=19(remember we started at n=0)


{{{a[19]=2(19)+2=38+2=40}}}


So the term {{{a[n]=40}}}


Now lets evaluate the sum

{{{s=(20/2)*(2+40)}}} Plug in values.  
{{{s=(10)*(42)}}}Simplify
{{{s=420}}} So the sum of the first 20 terms is 420.