Arithmetic Progressions

⭐ Important Questions

1. How many multiples of 4 lie between 10 and 250?
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   AP: 12, 16, 20, ..., 248\na = 12, d = 4, a_n = 248\n12 + (n-1)4 = 248 => 4(n-1) = 236 => n-1 = 59\nn = 60
2. Sum of first 7 terms of AP is 49, sum of first 17 terms is 289. Find sum of first n terms.
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   S_7 = 72(2a + 6d) = 49 => 2a + 6d = 14 => a + 3d = 7\nS_17 = 172(2a + 16d) = 289 => 2a + 16d = 34 => a + 8d = 17\nSubtracting: 5d = 10 => d = 2, a = 1\nS_n = n2(2 + (n-1)2) = n²