SEARCH HOME
Math CentralQuandaries & Queries

search

Question from Sara:

if the 6th term of an arithmetic sequence is 8 and the 11th term is -2, what is the first term?

Hi Sara,

In an arithmetic sequence the difference between successive terms is a constant, called the common difference. I sometimes think of these as steps between the terms. From the 6th term to the 11th term there are 5 steps. The 6th term is 8 and the 11th term is -2 so in your 5 steps from the 6th term to the 11th term you travel 10 units to the left on the number line. Hence the length of each step, the common difference is $\large \frac{-10}{2} \normalsize = -5.$ In most of the textbooks the common difference is denoted $d$ so for this example $d = -5.$

Can you find the first term now?

Write back if you need more assistance,
Penny

About Math Central
 

 


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS