Question 120780
Let's look at each consecutive pair and how you get from the first number to the second number. 
4-9: +5
9-17: +8
17-28: +11
28-42: +14
42-59: +17
Looks like you add 3 to the difference from the previous pair. 
The next pair would look like this,
59-?: +20
59+20=79.
The next number is 79. 
Now the pattern.
4-9: 5= 1*5
4-17: 13 = 5 + (5+3) = 2*5 + 3
4-28: 24 = 5 + (5+3) + (5+3+3) = 3*5 + 3*3
4-42: 38 = 5 + (5+3) + (5+3+3) + (5+3+3+3)=4*5+6*3 
4-59: 55 = 5 + (5+3) + (5+3+3) + (5+3+3+3) + (5+3+3+3+3) =5*5+10*3 
4-79: 66 = 5 + (5+3) + (5+3+3) + (5+3+3+3) + (5+3+3+3+3) + (5+3+3+3+3+3)=6*5+15*3 
The formula for the nth term would look like 
{{{a[n]=4+(n-1)*5 +  3*sum( n-1, 0, n-1 )}}}
You can simplify the sum term since
{{{sum( n-1, 0, n-1 )=((n-1)(n-2))/2}}}
Since we have n-2, this simplification only applies for n>1. 
For n=1, the sum equals zero.
{{{a[1]=4+(1-1)*5 +  0}}} 
{{{a[1]=4}}}
Therefore
{{{a[n]=4+(n-1)*5 +  3*((n-1)(n-2))/2}}}
{{{a[n]=4+(n-1)*(5 +  3*(n-2)/2)}}} for n>1
and 
{{{a[1]=4}}}
Check the answer with a couple of points to make sure everything looks good.
2nd term : n=2
{{{a[n]=4+(n-1)*(5 +  3*(n-2)/2)}}}
{{{a[n]=4+(2-1)*(5 +  3*(2-2)/2)}}}
{{{a[n]=4+(1)*(5)}}}
{{{a[2]=9}}}
5th term : n=5
{{{a[n]=4+(n-1)*(5 +  3*(5-2)/2)}}}
{{{a[5]=4+(4)*(5 +  3*(3)/2)}}}
{{{a[5]=4+(4)*(19/2)}}}
{{{a[5]=4+(38)}}}
{{{a[5]=42}}}
The asnwers check out to the originals.