 Hello and welcome to the session. In this session we discuss the following question which says sum of n terms of an AP is 5n square minus 3n, find the AP, hence find its 10th term. Now let's move on to the solution. First let Sn denote the sum of first n terms of an AP and we are given that Sn is equal to 5n square minus 3n. Since Sn is the sum of first n terms of an AP, so Sn minus 1 would be the sum of first n minus 1 terms of an AP. Let An be the nth term of AP. Now we have the nth term of an AP is given by Sn minus Sn minus 1. That is nth term of an AP is the difference of the sum to first n terms and the sum to first n minus 1 terms of the AP. Now since Sn is equal to this, so Sn minus 1 would be equal to 5n to n minus 1 square minus 3n to n minus 1 and this would be equal to 5n to n square minus 2n plus 1 minus 3n plus 3. That is we have Sn minus 1 is equal to 5n square minus 10n plus 5 minus 3n plus 3. So we get Sn minus 1 is equal to 5n square minus 13n plus 8. So now we have An that is the nth term is equal to Sn that is 5n square minus 3n minus Sn minus 1 that is 5n square minus 13n plus 8. So this would be equal to 5n square minus 3n minus 5n square plus 13n minus 8. So 5n square and minus 5n square gets cancelled. So we are left with 10n minus 8 that is the nth term of the AP that is An is equal to 10n minus 8. Now since we need to find the AP, so first let's take n equal to 1 in An. So we get A1 equal to 10 into 1 minus 8 and this would be equal to 2 that is the first term of the AP is 2. Now let's take n equal to 2 in An. So this would give us A2 equal to 10 into 2 minus 8 that is equal to 20 minus 8 and this is equal to 12. So 12 is the second term of the AP. Similarly on putting n equal to 3 in An we get A3 equal to 10 into 3 minus 8 that is equal to 30 minus 8 and this is equal to 22. So in the same way we can find out the rest of the terms of the AP and the common difference D is given by A2 minus A1 that is equal to 12 minus 2 equal to 10. This is the common difference of the AP. So now the AP is 2, 12, 22 and so on. Now we need to find the 10th term of the AP. So we have A10. Now this would be equal to 10 into 10 minus 8 by putting n equal to 10 in this. So we get A10 equal to 10 into 10 minus 8 that is equal to 100 minus 8 which is equal to 92. Thus the final answer is AP is 2, 12, 22 and so on and the 10th term of the AP is 92. So this completes the session. Hope you have understood the solution for this question.