SOLUTION: Using the following sequence,determine what type of function describes the sequence. Once you determine the type of function,find the function algebraically.(4,9,17,28,42,59,...)

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Question 120780: Using the following sequence,determine what type of function describes the sequence. Once you determine the type of function,find the function algebraically.(4,9,17,28,42,59,...)
Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
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

You can simplify the sum term since

Since we have n-2, this simplification only applies for n>1.
For n=1, the sum equals zero.

Therefore

for n>1
and

Check the answer with a couple of points to make sure everything looks good.
2nd term : n=2

5th term : n=5

The asnwers check out to the originals.