Find the sum of first n terms of an AP whose n th term is 5n-1.Hence find the sum of first 20 terms.

Find the sum of first n terms of an AP whose n th term is 5n-1.Hence f

1.	Find the sum of first n terms of an AP whose n th term is 5n-1.Hence find the sum of first 20 terms.
Answer» Ans.\xa0Let\xa0first\xa0term\xa0of\xa0A.P\xa0is\xa0a\xa0and\xa0common\xa0difference\xa0is\xa0d.Given\xa0:\xa0an\xa0=\xa05n-1So,\xa0a1\xa0=\xa05×1-1\xa0=4a2\xa0=\xa05×2\xa0-1\xa0=\xa09Common Difference (d) = 9-4 = 5Sum\xa0of\xa0first\xa0n\xa0terms\xa0Sn\xa0=\xa0n22×4\xa0+\xa0(n-1)\xa0×5=>\xa0Sn\xa0=\xa0n2(8\xa0+5n\xa0-\xa05)=>\xa0Sn\xa0=\xa0n23+5nSum\xa0of\xa0First\xa020\xa0Terms\xa0S20\xa0=\xa0202(3+5×20)\xa0=\xa010×\xa0103\xa0\xa0=1030 Given: an = 5n-1a = 5 x 1 - 1 = 5 - 1 = 4a2 = 5 x 2 - 1 = 10 - 1 = 9a3 = 5 x 3 - 1 = 15 - 1 = 14Therefore, AP is 4, 9, 14, .......Here, a = 4 and d = 5S20 = (20/2)[2 x 4 + (20 - 1) x 5] = 10 [8 + 95] = 10 x 103 = 1030Therefore, sum of 20 terms of given AP is 1030