The sequence 2,6,12,30,42... is called a rectangular number pattern because the terms can be visualized as a rectangular arrangements of dots. Create an expression to find the nth term and describe how it relates to the pictures of the dots above.

Question

natnat02 · Answer

attachment

jim_thompson5910 · Answer

Hint: notice how there is a pattern going on

we have rectangles of these dimensions
1x2
2x3
3x4
4x5
5x6
6x7

natnat02 · Answer

I saw that but how would I write the equation?

jim_thompson5910 · Answer

the 1st rectangle has the first dimension being 3
the 2nd rectangle has the first dimension being 3
the 3rd rectangle has the first dimension being 3
the 4th rectangle has the first dimension being 4
and so on

so the nth rectangle will have the first dimension being n where n is some unknown positive whole number

jim_thompson5910 · Answer

the next dimension is 1 more than the first dimension
if the first dimension is n, then the second is n+1

agreed?

natnat02 · Answer

yes thank you

jim_thompson5910 · Answer

so you simply multiply out n and (n+1)

n*(n+1) = ????

natnat02 · Answer

Thank you so much

jim_thompson5910 · Answer

what do you get when you multiply n and (n+1) ?