SEARCH HOME
 Math Central Quandaries & Queries
 Question from shauna, a student: The first five numbers in a sequence are 40, 37 34, 31, 28 Find an expression for the nth number in the sequence. Please could you explain to me what I have to do for the question. Thanks for your help. Shauna

Hi Shauna,

I'm going to illustrate with a different problem.

Find an expression for the nth term of the sequence 13, 17, 21, 25, 29, ...

The ... indicates that the pattern continues indefinitely. The pattern I see is that each term is 4 more than the previous term.

1. first term 13

2. second term 13 + 4 = 17

3. third term 17 + 4 = 21

4. fourth term 21 + 4 = 25

5. fifth term 25 + 4 = 29.

So it's easy to continue, just add 4 to each term to get the next term. But what if you want to know the tenth term without having to go through the ten steps to get to it? Can you find the tenth term in one step?

Look at the steps above, The first term is 13. For the second term you added 4. For the third term you added 4 twice (13 + 4 + 4). For the fourth term you added 4 three times and so on

1. first term 13

2. second term 13 + 4 = 17

3. third term 13 + 2 × 4 = 21

4. fourth term 13 + 3 × 4 = 25

5. fifth term 13 + 4 × 4 = 29.

so the tenth term is 13 + 9 × 4 = 13 + 36 = 49.

The question was to find the nth term so now I know the nth term is

13 + (n - 1) × 4

After all that here is my answer to my question.

The first term is 13 and each term is 4 more than the previous term so the nth term is 13 + (n - 1) × 4.

Penny

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