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InterviewSolution
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The general term of a sequence is given by an = -4n + 15. Is the sequence an A.P.? If so, find its 15th term and the common difference. |
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Answer» Given, an = -4n + 15 Now putting n = 1, 2, 3, 4 we get, a1 = -4(1) + 15 = -4 + 15 = 11 a2 = -4(2) + 15 = -8 + 15 = 7 a3 = -4(3) + 15 = -12 + 15 = 3 a4 = -4(4) + 15 = -16 + 15 = -1 We can see that, a2 – a1 = 7 – (11) = -4 a3 – a2 = 3 – 7 = -4 a4 – a3 = -1 – 3 = -4 Since the difference between the terms is common, we can conclude that the given sequence defined by an = -4n + 15 is an A.P with common difference of -4. Hence, the 15th term will be a15 = -4(15) + 15 = -60 + 15 = -45 |
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