The sum of first n terms of an ap is 5n^2-3n. Find it\'s nth and 10th

1.	The sum of first n terms of an ap is 5n^2-3n. Find it\'s nth and 10th terms
Answer» Given, Sum of n terms of AP (Sn) = 5n2\xa0- 3nHence, Sum of (n - 1) terms of given AP isSn - 1\xa0= 5(n - 1)2\xa0- 3(n - 1){tex}\\Rightarrow{/tex}\xa0Sn - 1\xa0= 5(n2 - 2n + 1)\xa0- 3n + 3Or, Sn-1\xa0= 5n2\xa0- 10n + 5 - 3n + 3 = 5n2\xa0- 13n + 8We know that,\xa0nth term of AP is given by :-an\xa0= Sn\xa0- Sn - 1\xa0= (5n2\xa0- 3n) - (5n2\xa0- 13n + 8){tex}\\Rightarrow{/tex}\xa0an\xa0= 10n - 8{tex}\\therefore{/tex}\xa01st term of AP = 10\xa0×\xa01 - 8 = 2 2nd term of AP = 10\xa0×\xa02 - 8 = 123rd term of AP = 10\xa0×\xa03 - 8 = 22{tex}\\therefore{/tex}Required AP is 2, 12, 22, 32...........Now, 10th term of A.P isa10\xa0= 10\xa0×\xa010 - 8 = 100 - 8 = 92

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