I'm Bon Crowder and the photos above are both of me - in 1989 and today. I'm a Generation X mom of Generation Z kids.

I began peer tutoring in high school in 1984. MathFour.com is the 2015 version of me helping peers be comfortable in math.

If you're a Gen-X parent, you're in the right place!

Hi Bon,

Have had lots of questions, just real busy and so I am faking it till I can make it.

How do I know if a set is closed under the rule of addition, same question for multiplication? Thought I understood it, guess I was wrong because I missed all 5 problems on a test.

Thanks for your help.

Thanks, Kellie! I’ve responded with this post.

Hi I got a question. I’m trying to find the recursive function for this sequence 1,7,21,43,73,111,157,211 but can’t seem to get it. How do I go about?

I’m going to type out my thinking as I go, so you can watch it happen…

1->7 (difference of 6)

7->21 (diff of 14)

21->43 (diff of 22)

43->73 (diff of 30)

73->111 (diff of 38)

111->157 (diff of 46)

157->211 (diff of 54)

Hmm…

1->7 (difference of 6=2*3)

7->21 (diff of 14=2*7)

21->43 (diff of 22=2*11)

43->73 (diff of 30=2*3*5)

73->111 (diff of 38=2*19)

111->157 (diff of 46=2*23)

157->211 (diff of 54=2*3*3*3)

Hmm…

1->7 (difference of 6=2*3)

7->21 (diff of 14=2*7)

21->43 (diff of 22=2*11)

43->73 (diff of 30=2*15)

73->111 (diff of 38=2*19)

111->157 (diff of 46=2*23)

157->211 (diff of 54=2*27)

Aha! Now I see a pattern! The difference of each is 2*number where the number increases by 4 each time.

In a fancy formula, they each differ by 2*(3+4n).

So the 1st term is 1.

The 2nd term is 7, which is 1+2*(3+4(2-2))

The 3rd term is 21, which is 7+2*(3+4(3-2))

The 4th term is 43, which is 21+2*(3+4(4-2))

The 5th term is 73, which is 43+2*(3+4(5-2))

…

And the nth term is the (n-1)th term+2*(3+4(n-2))

That was indeed a tough one!

Thanks Sandra!

I have a quick question about an explicit formula that does not have a common difference. How would I come up with a formula that had a number sequence of 1, 4, 10, 19… for expample. (each number going up by 3, 6, 9, 12..)

You’re starting at 1, so that’s your “seed.”

Then you’re going up by multiples of 3.

Maybe try nth term is (n-1)th term + 3n. Play with that idea.