Here are the first four terms of a sequence. 4
11
22
37
Find an expression, in terms of n, for the nth term of this sequence.

Step-by-step explanation:

We observe that the difference of terms is 4, 7 and 15 and next level difference is 4. It means the sequence is quadratic.

We can compare this with simple quadratic sequence

and find out that doubling each term gives us

This is close to our sequence, write the terms as follows to find exact rule

The first term:

The second term

The third term:

The fourth term:

The nth term as per observation above is:

-14

step-by-step explanation:

2x2 – 2(x+4)

=2x2-2（5+4）

=4-2×9

=4-18

=-14