Answer:
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.
