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Class 10 > Learn Mathematics > Determine the A.p whose third term is 16 and the difference...
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Determine the A.p whose third term is 16 and the difference of 5th from 7th term is 12?

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an= a+(n-1)d an=10+(30-1)*(-3) =10-87=-77 30th term is -77 a + (3 ? 1) d = 16 a + 2d = 16 ... (i) a7 ? a5 = 12 ? = 12 (a + 6d) ? (a + 4d) = 12 2d = 12 d = 6 From equation (i), we get, a + 2 (6) = 16 a + 12 = 16 a = 4 Therefore, A.P. will be 4, 10, 16, 22, …
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an= a+(n-1)d an=10+(30-1)*(-3) =10-87=-77 30th term is -77 a + (3 ? 1) d = 16 a + 2d = 16 ... (i) a7 ? a5 = 12 [a+ (7 ? 1) d] ? [a + (5 ? 1) d]= 12 (a + 6d) ? (a + 4d) = 12 2d = 12 d = 6 From equation (i), we get, a + 2 (6) = 16 a + 12 = 16 a = 4 Therefore, A.P. will be 4, 10, 16, 22, … read less
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