N j 1n j 1 j n j n n j 1n

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Unformatted text preview: ,k≥0 2k + 1 4. 1 3 9 27 ,− , ,− ,... 2 4 8 16 2 Math fans will delight to know we are basically talking about the ‘countably infinite’ subsets of the real number line when we do this. 3 Sequences which are both arithmetic and geometric are discussed in the Exercises. 9.1 Sequences 555 Solution. A good rule of thumb to keep in mind when working with sequences is “When in doubt, write it out!” Writing out the first several terms can help you identify the pattern of the sequence should one exist. 25 1. From Example 9.1.1, we know that the first four terms of this sequence are 1 , 5 , 27 and 125 . 39 81 To see if this is an arithmetic sequence, we look at the successive differences of terms. We 5 25 5 find that a2 − a1 = 9 − 1 = 2 and a3 − a2 = 27 − 9 = 10 . Since we get different numbers, 3 9 27 there is no ‘common difference’ and we have established that the sequence is not arithmetic. To investigate whether or not it is geometric, we compute the ratios of successive terms. The first three r...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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