Question

Find the common difference (d) of the arithmetic sequence. It it is not arithmetic, enter "None" in the box. 10, 2, -6, -14, -22, ... d =?​

Answer 1

Answer:  d = -8

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Explanation:

Pick any term that isn't the first term. Then subtract off the previous term. If we get the same result each time, then the sequence is arithmetic, and that result is the common difference.

• term2 - term1 = 2-10 = -8
• term3 - term2 = -6-2 = -8
• term4 - term3 = -14-(-6) = -14+6 = -8
• term5 - term4 = -22-(-14) = -22+14 = -8

We get -8 each time, so the sequence is arithmetic with common difference d = -8. It says to add -8 to each term to get the next term. This is the same as subtracting 8 from each term to get the next term.

Note how:

• 10-8 = 2
• 2-8 = -6
• -6-8 = -14
• -14-8 = -22