Arithmetic, like life, sometimes involves solving problems. An arithmetic sequence is a series of numbers that each differ by a constant amount. When you are deciphering an arithmetic sequence to the first six terms, you are simply figuring out the code and translating it into a string of six numbers or arithmetic expressions.

## Apply the Difference

In some arithmetic sequence problems, you'll know the first number and the constant difference to apply to all subsequent numbers in the sequence. The first number is often given a symbol, such as a1, but it can be called anything. Similarly the distance is frequently expressed a d, but it can be represented as any letter. If you know a1=10 and d=3 then you add three to each number in your sequence to find the next. Your sequence is, therefore, 10, 13, 16, 19, 22 and 25.

## Solve the Equation

Some arithmetic sequences have you solve an equation to crack the code. For example, if you are given something like a_n=10 + (n-1)1.75, and you know that the first number, a1=10, then you solve for a2, a3, a4, a5 and a6. In this equation, a_n refers to all the numbers in the sequence, so if you are figuring out what the second number in the sequence is, for example you substitute a 2 wherever you see an n. For a2, the equation is 10+(2-1)1.75 or 11.75. For a3, the equation is 10+(3-1)1.75 or 13.50 and so forth.

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About the Author

Brenda Scottsdale is a licensed psychologist, a six sigma master black belt and a certified aerobics instructor. She has been writing professionally for more than 15 years in scientific journals, including the "Journal of Criminal Justice and Behavior" and various websites.

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