Answer :
Final answer:
The nth term of the given arithmetic progression (AP) is 3 + (6n-6), and the 15th term can be found by plugging in n = 15 into the nth term formula.
Explanation:
The sum of the first n terms of an arithmetic progression (AP) can be found using the formula Sn = n/2(2a + (n-1)d), where Sn is the sum, a is the first term, and d is the common difference. Comparing this with the given expression 3n² + 6n, we can see that a equals 3 and d equals 6.
Therefore, the nth term is given by tn = a + (n-1)d, which can be simplified to tn = 3 + (6n-6). To find the 15th term, substitute n = 15 into the nth term formula: t15 = 3 + (6(15)-6). Solving this gives you the value of the 15th term.
