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Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers),[2] structure,[3] space,[2] and change.[4][5][6] There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.[7][8] If a sequence of values follows a pattern of adding a fixed amount from one term to the next, it is referred to as an arithmetic sequence. The number added to each term is constant (always the same).
The fixed amount is called the common difference, d,referring to the fact that the difference between two successive terms yields the constant value that was added. To find the common difference, subtract the first term from the second term. 1. Find the common difference for this arithmetic sequence 5, 9, 13, 17 ... | 1. The common difference, d, can be found by subtracting the first term from the second term, which in this problem yields 4. Checking shows that 4 is the difference between all of the entries. | 2. Find the common difference for the arithmetic sequence whose formula is an = 6n + 3 | 2. The formula indicates that 6 is the value being added (with increasing multiples) as the terms increase. A listing of the terms will also show what is happening in the sequence (start with n = 1). 9, 15, 21, 27, 33, ...
The list shows the common difference to be 6. | 3. Find the 10th term of the sequence 3, 5, 7, 9, ... | 3. n = 10; a1 = 3, d = 2
The tenth term is 21. | 4. Find a7 for an arithmetic sequence where a1 = 3x and d = -x. | 4. n = 7; a1 = 3x, d = -x | 5. Find t15 for an arithmetic sequence where t3 = -4 + 5i and t6 = -13 + 11i | 5. Notice the change of labeling from a to t. The letter used in

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