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Write the algebra of the following sequences and its sum of n terms 1.5, 10, 15, 20, ……….. 2. 6, 11, 16, 21, ……… 3. 4, 9,14,19, ………. 4. 3, 8, 13, 18, ………….. |
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Answer» 1. 5, 10, 15, 20, First term f = 5 Common difference = d = 10 – 5 = 5 General form xn = dn + (f – d) = 5n + (5 – 5) = 5n xn = 5n Sum = \(\frac{1}{2}\)n(x1 + xn) = \(\frac{1}{2}\)n(5 + 5n) = \(\frac{5}{2}\)n(n + 1) 2. 6, 11, 16,21, ………….. First term f = 6 Common difference d = 11 - 6 = 5 General form xn = dn + (f - d) = 5n + (6 - 5) = 5n xn = 5n + 1 Sum = \(\frac{n}{2}\)(x1 + xn) = \(\frac{n}{2}\)(6 + 5n + 1) = \(\frac{n}{2}\)(5n + 7) 3. 4, 9, 14, 19, …………. First term f = 4 Common difference d = 9 - 4 = 5 f - d = 4 - 5 = -1 General form xn = dn + (f - d) xn = 5n - 1 Sum = \(\frac{n}{2}\)(x1 + xn) = \(\frac{n}{2}\)(4 + 5n - 1) = \(\frac{n}{2}\)(5n + 3) 4. 3, 8, 13, 18, ………… First term f = 3 Common difference d = 8 - 3 = 5 f - d = 3 - 5 = -2 General form xn = dn + (f - d) xn = 5n - 2 Sum = \(\frac{n}{2}\)(x1 + xn) = \(\frac{n}{2}\)(3 + 5n - 2) = \(\frac{n}{2}\)(5n + 1) |
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