Find the nth term of 3,12,27,48,75

3n^2

Step-by-step explanation:

3, 12, 27, 48, 75

List the differences between terms:-

9, 15, 21, 27

Now find the second differences:-

6, 6, 6

The sequence in the question is quadratic and the first coefficient (that of n^2) = 6/2 = 3. The first term in the nth term formula is 3n^2.

Now we write out the original sequence and the 3n^2 values as follows:-

3 12 27 48 75

3 12 27 48 75

They are the same so the formula for the nth term is 3n^2.