   SEARCH HOME Math Central Quandaries & Queries  Question from Rookin, a student: Can you help me find the nth term for this ... 20,17,14,11,8 i'm really confused oh and could you also tell me how you got the answer? We have three responses for you

Rookin,

If you can find a ruler in centimeters, locate the 20, the 17, the 14, the 11, the 8 and try to guess the next number.

Claude

Rookin,

Claude's suggestion should help you see how to get from each term to the next. The next term will be the sixth term. How can you get from the first term, 20, to the sixth term in one step? How can you get from the first term to the nth term in one step?

Harley

Hi Rookin.

I'll show you a similar solution. What is the nth term of 10, 5, 0, -5, -10, -15,...?

First I look at the difference between adjacent terms: in each case, the right term is 5 less than the left term.

That means that the second term is 5 less than the first and the third term is 10 less than the first. I suppose you could say that the zero'th term is 5 more than the first term, so it would be 15 if it was listed in the sequence.

In fact, I can tell the value of the nth term just by knowing how many times to subtract five from the zero'th term.

0th term: 15 - (5x0)
1st term: 15 - (5x1)
2nd term: 15 - (5x2)
3rd term: 15 - (5x3)
4th term: 15 - (5x4)
...
nth term: 15 - (5xn) = 15 - 5n.

You can solve your problem the same way, Rookin.

Stephen.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.