Math CentralQuandaries & Queries


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,

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