hi, my name is umar i am a student in collage.
my question is what is the nth term for a house of cards 4 stories high if you use the following numbers:
2 7 15 26
Please help me.
thank you

 

Umar,

You can use differences to see how to generate the terms in the sequence.

sequence 1   7   15   26
first differences   5   8   11  
second differences     3   3    

If the second differences are all 3's then I can see how to generate the next term. The next second difference is 3 so the next first difference is 11 + 3 = 14 and thus the next term in the sequence is 14 + 26 = 40.

sequence 1   7   15   26   40
first differences   5   8   11   14  
second differences     3   3   3    

And now you can generate the next term and so on but you asked for an expression for the nth term. To do this I need some notation. I am going to call the nth term of the sequence xn and the nth first difference dn . Then the table of differences around the nth term looks like

sequence xn-2   xn-1   xn
first differences   dn-1   dn  
second differences     3    

Thus

dn = xn - xn-1
dn-1 = xn-1 - xn-2 , and
dn - dn-1 = 3

Substitute the values for dn and dn-1 from the first two equations into the third equation and solve for xn. This will give you an expression for xn in terms of xn-1 and xn-2.

Penny