The sum the first n terms of an AP is (3n²+6n). Find the n th terms and the 15 th terms of this AP.

The sum the first n terms of an AP is (3n²+6n). Find the n th terms a

1.	The sum the first n terms of an AP is (3n²+6n). Find the n th terms and the 15 th terms of this AP.
Answer» Here it is given that sum of first n terms\xa0is equal to Sn\xa0= 3n2\xa0+ 6n\xa0Now,\xa0Sn-1\xa0= 3(n - 1)2\xa0+ 6(n - 1)= 3(n2\xa0- 2n + 1) + 6n - 6= 3n2\xa0- 6n + 3 + 6n - 6= 3n2\xa0- 3Therefore nth term, Tn\xa0= Sn\xa0- Sn-1\xa0= 3n2\xa0+ 6n - 3n2\xa0+ 3= 6n + 3And, 15th term T15\xa0=\xa06(15) + 3= 90 + 3 = 93Therefore nth\xa0term is 6n+3 and 15th\xa0term is 93