Determine whether a Sequence is an AP or not
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 Determine whether a Sequence is an A.P. or not Arithmetic Progression: An arithmetic progression or arithmetic sequence, is a sequence of numbers such that the differences between two successive terms is always a constant . For example, the sequence 1,5, 9, 13, 17, 21... is an arithmetic progression with common difference 4. ALGORITHM STEP I Obtain an STEP II Replace n by (n + l) in an to get an + 1 STEP III Calculate an + 1- an STEP IV Check the value of an+ 1- an. lf an+ 1- an is independent of n, then the given sequence is an A.P. Otherwise it is not an A.P. Following examples will illustrate the above algorithm.
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 Example 1: Show that the sequence defined by an = 4n + 5 is an A.P. Also, find its common difference. Solution: you have,          an = 4n + 5. Replacing n by (n + 1), we get          an + 1 = 4(n + 1) + 5 = 4n + 9 Now, an + 1 - an = (4n + 9) - (4n + 5) = 4 Clearly, an + 1 - an is independent of n and is equal to 4. So, the given sequence is an A.P. with common difference 4. Example 2: The nth term of a sequence is 3n - 2. Is the sequence an A.P. ? If so, find its 10th term. Solution: you have an = 3n - 2. Clearly an is a linear expression in n. So, the given sequence is an A.P. with common difference 3. Putting n = 10, you get a10 = 3 * 10 - 2 = 28. so the 10th term will be 28.

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